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" Methinks it should have been impossible 
Not to love all things in a world like this, 
Where even the breezes and the common air 
Contain the power and spirit of harmony." 


No. 332, Pennsylvania avenue, 



.C *£ 

Entered according to an act of Congress, in the year 1860, 
by Samuel Elliott Coubs, in the Clerk's office of the 
District Court of the District of Columbia. 

Printed by R. A. "Waters, Washington, D. C . 











The following remarks are offered at the outset, in order that the character 
of the Work, its range of subject, and the circumstances under which it is 
published may be knoAvn at once. 

The author is not, in business or avocation, devoted to science. He has, what 
is supposed to be, a more practical pursuit. These " Studies of the Earth" 
were indulged in for many years as the recreation of leisure hours, — these lei- 
sure hours often having been few and far between. The work, therefore, has 
the characteristic faults, errors, and short comings which must needs arise from 
a want of continuous effort and of an absorbing application to the subject. 
These imperfections, however, to some degree at least, are offset by peculiar 
advantages. They, who make a business of science, are inclined to be quite 
well satisfied with the received hypotheses, — overvalueing, perhaps, the coin 
which has "the image aud superscription of the Csesars of the science." Be- 
sides, professed students of science, in most instances, necessarily, are confined 
to a limited range of investigation ; nature is so vast in its dimensions that one 
field only can be cultivated successfully, so as to yield " a living" by its pro- 
ducts. There are, therefore, thorough geographers, learned geologists, and pro- 
found astronomers, all of whom are, doubtless, doing the world good service, 
who, restricted in the range of their enquiries, do not attempt even to discover 
the relations of the different classes of facts belonging to the separated enclo- 
sures of investigation ; while, on the other hand, these relations may be dis- 
covered by a student of science who has taken a more enlarged view of nature, 
even if he have not a thorough and unmistaking comprehension of all the facts 
which form the subject of the closer examination of the experts in their several 
chosen specialities. 

The separation of the facts of integral nature into artificial divisions has 
advantages compensating, perhaps, for its consequent evils. The more narrow 
the range of the eye the more distinct is its vision. It is not seldom, however, 
that the unity of the laws of nature, even, is also broken up ; independent 


tribunals being established for the departments, while there is no superior 
court of appeal from the local jurisdictions. The result of this is altogether 


" Caelum non animum mutant, qui trans mare curruntP Condition and action 
unchanged by place is the characteristic of mind ; superlatively is it an attri- 
bute of the mind of God, who, in passing, in creative energy, over the sea of 
space, changes not the creative idea. The system of worlds, each world of the 
system, every division of the world, its separate elements, and constituent 
masses, are parts of a whole, and, as the varying tints of the coloring of a 
picture and all the separate touches of the pencil combine as one color, as one 
touch, for the development of an idea, so God's great Idea subdues all these 
parts of the universe into one perfectly harmonious whole. 

Useless, almost, are the minor theories and sub-hypotheses which, by the 
expert in magnetism, are applied to explain the polarity of the needle, or 
which, by the astronomer, are aj>plied to explain the direction of the axis of the 
earth. The needle has its daily, its annual, and its secular variation from a 
mean to which after many years it returns ; the pole of the earth, sweeping 
around the sun for twenty-five thousand years ; bowing annually in declina- 
tion to the sun, bending back and forth every twenty years as if in response to a 
motion of the moon, ever quivering in space as if without fixed aim ; neverthe- 
less, as it now points, after another of the long periods has passed away, it will 
again point to the same identical dot of the heavens ; the majestic earth and 
the tiny bit of steel wire both surely and safely guided by one principle, return, 
after long periods of oscillation, to the law-determined direction. 

The phrase " physical cause" is a contradiction of terms ; it means only a 
fixed sequence of facts ; and, under this right construction, the apparently 
most fundamental physical theory, say that of universal gravitation, is not the 
expression of a cause, but of an effect, not of power, but of a result or phase of 
the action of a spiritual cause. It was so regarded by its author, Newton, and 
to this faith, the great minds of Europe have returned, as is stated in a late 
opening address before the British Association. 

It can hardly be said that nature presents itself under two divisions even ; 
it is more correct to say, that nature presents itself under two aspects. Nature 
brings to light and exhibits fundamental or ultimate laws ; and, besides, it dis- 
plays the facts of the universe, as arranged in divisions and subdivisions, under 
these laws. What is intermediate between truth and facts is the growth 
of the human mind. It is to be regarded as mere scaffolding, to be thrown 
aside when the building is completed ; hypotheses are the morning's clouds 


which are the reflecting medium of the dawn of day; the risen sun drying up 
these wreaths of vapor. 

Impressed by these views, the author, as his stand point, assumes three 
positions which are the branches of one fundamental truth. The first of these 
positions is : the areas, contours, and relative positions of the terrestrial masses 
of land and water, are fully and completely determined by law, — nothing enter- 
ing into the earth's structure which is in the least degree, fitful, capricious, or 
accidental; the second is: the structure of the earth is in consequence of the 
laws which also determine the magnitudes, velocities, and relative positions of 
the spheres of the solar system ; the third is : the astronomical elements of 
the earth are, in their existences and values, the parts of a system which is so 
faultless in its symmetry that any one of these elements can be calculated from 
the others ; and this, without reference to any physical causes for these elements 
which actually exist or which are hypothetically assumed to exist. 

These positions, philosophically, as abstract truth, will be admitted by 
by every healthy and normal mind. They are true because of the existence of 
God who leaves nothing out of the pale of laws which extend in their range 
of action from the heavens above to the earth beneath, — resulting in the gift 
of a complete and beautiful unity to the entire creation. Doubt dares not lay 
his tremulous hand on them. The only question is, whether, and to what ex- 
tent, the facts of nature can be shown to be the reflection of these laws. 

It is in vain to strive to make the clay-cold facts of nature tell of the principles 
by which they are formed, and by which they are combined one with the other. 
They have of themselves no speech nor language. Like the collections of a 
naturalist, the specimens are dead and motionless ; they must be warmed by 
the glow of truth ; they must be bathed by the flow of thought over them ; then 
they revive into a common life and declare with common tongue, the complete- 
ness and harmony of the gradation of kinds, — each individual as a fact incom- 
plete, their union, perfection, and their united voice and common utterance, 

The sound philosophy which opens fundamental truth to the mind, also di- 
rects the course of the investigation by which this truth may be reflected back 
from the facts as they exist in nature to the mind, — thus changing attention from 
the will to the acts of God, from- the wisdom which creates, to the harmonv 
which ensues. It accordingly dictates that a prominent earth- division be se- 
lected for comparison with the planetary element which has the strongest anal- 
ogy with it. The two facts, — the one of the domain of Gea, and the other of 
the domain of Urania which are selected, are these: The telluric division is 


the earth's equatorial redundancy or the ellipticity of the figure of our globe ; 
and the planetary element is the eccentric annual path of the earth or the el- 
lipticity of its orbit around the sun. The analogy between these elements ap- 
pears in this : each of them determines a path of motion, — the figure of the 
earth modifying the orbits of the axial diurnal rotation of parts of the earth, 
the ellipticity of the path of the revolution of the planet around the Sun, being, 
in other words, a modification of the annual orbit ; the earth's figure and the 
form of its orbit constitute paths or orbits of motion, the one of the diurnal, 
the other, the annual motion of the earth. 

From the ellipticity of the earth's orbit or eccentricity of the sun's position 
in it results the fact, that one point of the orbit is the nearest to the sun. This 
point, — the earth's perihelion (or the sun's perigee), — is not located year after 
year at one special and fixed point of the orbit. 

The perihelion revolves aroulid the orbit ; the point of space which the 
earth occupied as its perihelion of this year will not be the point occupied as 
the perihelion of the next year, — this point of nearest approach to the sun, re- 
volving around the orbit, according to observation, in 110,340 years ; while 
the earth turns on its axis 365.24 times in every year of the period. 

On their first presentation these elements appear wide apart ; there is ap- 
parently an immense difference between them in relative magnitude and im- 
portance, and in their assigned physical causes and functions. The truth 
fills the void between them, and when seen in contact, as it were side by side, 
they lose their distinctive characters becoming the analogous conforming 
parts of one symmetrical structure. 

This is their relation : as the period of the year in days is to the period 
of the revolution of the ellipticity of the orbit or sun's perigee,so is the ellipti- 
city of the earth's figure, or its redundant equator, to the magnitude of the 
earth. In another form of expression ; as 5,455, the number of the miles of 
the annual advance of the perihelion of the orbit (or sun's perigee) is to 
1,647,950 (less -s-ot.t)) the daily velocity of the earth in its orbit, so is 26 ; 227 
miles, the value of the ellipticity of the earth's figure, to 7,937 miles, which 
is the value of the earth's diameter. 

If a man had been told that by travelling a certain number of miles in 
one direction, and thence a certain number of miles in another, he would find 
a certain house which he was in quest of, and the traveller, journeying according 
to these directions, found the house which he sought : would he prate, on 
his arrival, of accidental numerical coincidences and of the chance-result of his 
journey? It is taught by good authority that certain harmonic relations, exist 


by law, and will be discovered by a search for them in the direction which 
was indicated. Can common sense regard the fact, and the discovery of the 
fact, (the existence of which a priori was indicated, and the direction to which, 
pointed out by sound philosophy) as any approach toward the hap-hazard 
character ? Will not a sound judgment declare that there has been discovered 
a link of 

" The golden everlasting chain, 
Whose strong embrace holds heaven, earth and main" I — (Jliad.) 

What is the rationale for this, and how is it to be explained by the theo- 
ries and hypotheses of the school ? The author cannot reply to these questions 
because he knows of no sub-hypotheses or recognized physical theories which 
will cover the relation ; and, in his turn, he asks other questions : why is it that 
the right arm of a man so closely resembles in form and function the left arm '.' 
How is the fact explained, or under what physical law is it placed, that "the arm*" 
is gradually reduced in its form, function and character down, through grada- 
tions of animal life, until it is found in the rudimental arm of a reptile as an' 
apparently useless skin-enclosed appendage ? 

There are facts standing at the very threshold of science which, as founda- 
tion-facts supporting the vast fabric of nature, are too large, and too extensive 
to be covered over by what may be called local physical causes ; and such ar- 
range themselves under the elementary truths, or under the fundamental laws 
of nature. These facts are what they appear, have the forms they wear, because, 
as parts of a whole, they are clothed in a greater or less degree with the char- 
acter, aspect, and expression of the Great Entity of the material universe. 
The law establishing this whole or entity gave to its specialities a kindred 
aspect and a family character, and if a glimpse is caught of this expression, it 
is discovered that all the associated facts repeat and re-echo the expression ; 
for, while each individual entity or subdivision has an independent life, it has 
also a life common to all the specialities of existence. Beauty, as a gar- 
ment, without seam or rent, is not only wrapped around the whole, but it also 
closely fits, and comes into contact with all parts and members of the aggre- 
gated whole, (p. 81 et seq.). 

A priori therefore, from general principles it could have been safely asser- 
ted that there is a very close relation between the astronomic element by which 
the form of the earth's annual orbit, and the telluric element by which the or- 
bits of the axial rotation of parts of the earth are determined. Thus, ttu 


law declares the relation of the facts, and the facts laid side by side become as 
a mirror to throw back the light of fundamental truth into the mind. 

The discovery of this relation is indeed important, not only in itself, but 
as opening a new path of investigation which leads to truth far beyond the grasp 
and action of the physical causes. Nor is this assertion, in the least, an ex- 
hibition of vanity ; for the author has nothing to boast of in its discovery. 
A child led by the hand of a father may discover much not due to his own power 
of observation, so by grasping a known and fundamental truth the author was 
led to this fact of relationship. Milton wrote, " if virtue were weak, heaven 
would stoop to it." True, this is, in many senses. All that men know of the 
physical structure of the heavens or of the earth is because of simplicity of 
plan, — nature, as it were, stooping down to the comprehension of man. 

A connection being established between one astronomic element and one 
subdivision of the earth, this fact will open a path to a knowledge of the rela- 
tion of this subdivision of the earth (its excess of equator) to the lower sub- 
divisions, — those of the separate masses of land and areas of water lying on the 
surface of the globe; and these, afterwards, will be found also to be full 
of symmetrical relations to each other. 

The author was once asked : ' how can there be any plan or symmetry of 
the earth's surface-divisions when the blowing of the wind and the rushing of 
water scatter portions of the earth ; when rivers and ocean-currents wear 
away the land ; -when rocks continually disintegrate ; when earthquakes and 
volcanoes rend its surface' ? The questioner, a learned man, would hardly deny 
that a symmetrical form pertains to a statue because the saw, hammer, chisel, 
and rasp had been used in fashioning the statue from a rude block of stone. 
The sculptor had his idea and used tools to form the carving according to this 
idea. God has a constructive idea, and the winds and waves, the rivers and 
the ocean-streams, chemical action and the earthquake and volcanoe, are the in- 
struments used in developing the preconceived and ordained symmetry of the 
earth's structure. A contrary result would prove that God works without plan, 
or that He has such various facts to control that He is unable to make them 
co-work for carrying out His desired plan. 

Plan, method, order, symmetrical relations and co- working of parts exist 
every where throughout the whole creation. The surface of the earth, as an 
exception, is not left slovenly and disorderly. There is no accident in the 
earth's construction. This is certain truth. The only question, as before said, 
is of the penetration of science, — the only doubt, is of man's ability to trace out 


the harmony. The earth's structure appears, it is most true, to be the result 
''of the wildest caprice." A map of the world presents an appearance as if 
moistened clay had been thrown over the sheet, large parts of which, accident- 
ally separating, formed the irregularly shaped continents, and smaller parts, 
spattering about, became the islands and the groups of islands of diverse and 
strange configurations. The fault is in the eye of the observer ; it does not 
pertain to nature ; and the apparent capricious ness will vanish at once when 
the earth's surface is looked upon in the light of the principle of its structure. 

Most clearly and most assuredly a relation between one subdivision of the 
globe and one astronomical element exists : the magnitude of the earth repeated 
once for each and every day of the year equals in its sum the redundancy of 
its equatorial regions repeated once for each and every year of the period of 
the revolution of the perihelion of its orbit. This stands not alone ; the heav- 
ens do not reach down to the earth with this point of contact only. The relation 
is one link of a chain of harmony which, descending from above, coils in nu- 
merous folds around the earth, binding its subdivisions to each other, and its 
whole to the heavens. 

Throughout the whole of nature, there exists a step-by-step gradation of 
parts, with a preservation, down to the lowest, of the type, character or attri- 
butes of the superior form from which it descends. This gradation is deeply 
marked and palpably distinct in the subdivisions which are the subject of the 
present discussion. By this gradation the extent of the terrestrial masses can 
be calculated : 110,340 times the redundancy of the equator is equal to 365.24 
times the diameter of the earth ; 365.24 times this redundancy is equal to the 
next lower step of gradation, which is the maximum extent of the terrestrial 
masses. Thus, 365.24 times 26.227 is 9,584 miles, or 138° arc of the equatorial 
circumference of the earth at 69.2 miles to the degree, (p. 49), which value 
thus deduced from the foundation-principle of the system, — a regular gradation 
of form, — is the actual measure of the extent of the earth's surface divisions. 
In the first place, there are four north and south major axes of Continents, which 
axes are 90° apart, and which stretch from 54i° S. to 83 i° N. latitude, being 
equal to 138°, (p. 7, and map); secondly, the maximum breadth of the terres- 
trial masses, or east and west extents in difference of longitude, is 138°, (p. 12. 
p. 93, and map ) . This application of the measure in itself is sufficient to show 
the soundness of the principle by which it was evolved. 

But there is a most convincing and interesting feature of this measure 
shown by the manner of its application. The period of axial rotation, as ha* 


been shown, is an element of the extent of the terrestrial masses. The ve- 
locity of the axial rotation of the earth's surface is not of one degree ; it de- 
creases from the equator on either side to nil at the poles. If, therefore, the 
presented doctrine is sound, the extents of the terrestrial masses must be corres- 
pondingly reduced from the equator to the poles. It is so in nature. The 
measure of the extents of the terrestrial masses is 138° as arc of a great circle, 
or positively 9,584 miles at the equator only. On the other parallels the meas- 
ure is 138° arc of the circle of rotation or of difference of longitude. The extent 
of the terrestrial masses is determined by the velocity of axial rotation, and 
this extent decreases with the decrease of axial velocity. 

The rationale of the measure of the terrestrial masses, it is believed, can 
be clearly exhibited. The general system, the all-embracing whole, harmoni- 
ously complete in and of itself, is composed of parts which are sub-entities or 
sub-individualities. These parts, therefore, necessarily have a binary char- 
acter ; they have traits, attributes, or qualities which give individuality, and 
also those by which they are linked together as symmetrical members of the 
general system. The parts are as the limbs of an animal which have the 
binary or two-fold character, each one being adapted to a certain position and 
for a special function, yet it has also a character common to all, by which the 
separate members constitute the completeness of the entire organism ; poeti- 
cally, of the individual entities of nature : 

" Fades non omnibus una } _ 
Nee diversa tamen ; qualis decet esse sororum. ,y 

The orbit of the earth has its divisions or sub-entities, one of which is that 
part which is traversed by its perihelion in one year,, equal to TT -J )IT7 of the 
orbit, and another is that part of the orbit which is traversed by the earth 
itself in one day, equal to aVi.TT °f the orbit. The- earth has its subdivisions or 
individual entities, one of which is the redundancy of its equatorial regions, 
and another is of its surface structure — its terrestrial masses. The relation of 
the subdivisions of the orbit to the subdivisions of the earth is such, that TTTj ' IT? 
of the earth's magnitude is equal to 3 ±- T . 2 4 of the redundancy of its equator: 
and 3-| T .y T of the extent of the terrestrial masses, (9,584 miles,) is also equaf 
to the redundancy of the equator, (26.227 miles.) The gradation of the divis- 
ions of the earth is therefore united with the divisions of the orbit by a ratio of 

This gradation of forms or of sub-entities on the ratio of periods is a prin.- 


ciple most deeply inwrought into the fabric of the system. The harmonic law 
of Kepler is one phase of it. Each planet is a sub-entity of the system, and has 
its own special period and its own special existence. But planets are not iso- 
lated divisions of the system. Differing as they do in distance, in period, in 
ellipticity and eccentricity of orbit, in magnitude, axial velocity and inclination 
of axes, they become in harmony by the common ratio of periods and distan- 
ces ; and this is not all : each and every speciality pertaining to them has at- 
tributes or qualities or values by which it is brought into harmonious relation. 

The general bond of relationship, visible as it exists between the periods 
and the distances of the planets, also unites the specialities of all the sub- 
divisions of the system, although the connecting bonds may be unseen and 
unknown. This is unquestionably true. God, with power supreme, could not 
form a system in j^erfect integrity of form and character if any one of its parts 
were without affiliating attributes. It must be wrong and lead to other error, 
to consider that the distances of the planets possess a relation which other dis- 
tances have not, because there is no special or local legislation in nature. The 
spheres as individual worlds are constituted as one step only of a long and 
regulated descending gradation of parts. A law which applies to their dis- 
tances from the centre of their orbital revolution applies also to the earth 
(another step and descent) in the distance of its surface from the centres of the 
orbits of axial rotation ; and it applies also to the variations of the distance 
from the axis of the earth to its surface by its equatorial enlargement in the 
relative altitude of its surface-divisions. The generalisation is an echo of the 
voice of nature which, from every part of the structure, proclaims the simple 
grandeur of the creation which, in its unity and in its variety, in its form as jf 
whole, and in the character of its parts, is because of universal law, always the 
same in character and one in action and results. 

Each entity of the system becomes an individual separate part of it by the 
consent of motion, that is by the common velocity and direction of the motion, 
of all the matter of which it is composed. Each part or entity of the general 
system is thus separated from other parts in juxtaposition with it, by difference 
of motion ; or, in other words, the limit or extent, or distance of the part from 
the centre of its motion, is actually constituted by, or rather flows, as a neces- 
sary consequence from, the common motion of the matter of which it is consti- 
tuted. Plence, velocity and distance, in law-determined ratios, are inseparably 
and universally connected." Velocity and distance (which latter gives the 
range or extent of the motion of the parts of the system in retrogressive orbits) 
constitute periods ; there is assigned to each entity that special degree of velo- 


city which, associated with its special distance, results in a period which is one 
of the system of periods by which the relative position of all parts of the 
edifice of worlds is established. The law of the relation of distance and veloci- 
ty, (of which Kepler's is one action), is necessary to preserve the integrity of 
form and oneness of character of the general system, and thus to constitute a 
Perfect Whole. The system of periods necessarily embraces the periods of all 
parts, from the primary divisions down to the lowest aggregate of matter which 
has common motion constituting it an entity or individual part of the system. 
The worlds do not consist of, nor could they possibly be created from mere brute 
matter, having extensive magnitude of parts, form, density, and so on. There 
must be, and necessarily is, combined with the material of worlds, — a " some- 
thing" which approaches toward the character of the spiritual, — an addition 
which gives to it its life and its soul. Time, — mysterious time, of itself not 
the subject of distinct thought, palpable, and intelligible only, by its associa- 
tion with matter in the relative velocity of the parts of the system, vivifies 
all the limbs, members, and parts of the great organism, giving to the varia- 
tions of form, magnitude, and relative extent their harmonious relations of 
structural affinity, (p. 8) ; stubborn matter, as existing in diverse forms, ex- 
tents and positions of parts, by the aetion of time becomes, as it were, plastic 
and yielding, and is moulded into a symmetrical creation. 

There is a most beautiful instance of the union of diverse and otherwise 
conflicting entities by the ratio of their periods, the citing of which is better 
than an essay on the subject: The excess of the earth's equatorial circumfer- 
ence is, according to the doctrine of Gradation of Forms, an individual entity. 
By it, the orbit of the earth's axial equatorial rotation is enlarged 82.47 miles. 
In 110,340 days (302.1 years) this addition of motion to the earth's equator, 
becomes, in its repetition, equal to the annual velocity of the earth's axial rota- 
tion or 365.24 times its circumference. In 110,340 years, the redundancy adds 
365.24* times the circumference of the earth ; and in this period the ellip- 
ticity of the earth's orbit completes its revolution around the orbit of the 
earth, (p. 50) . Thus the relative velocity assigned to these diverse and varying 
extents results in periods by which these entities become relatively in the same 
position, or coincident or concomitant, in fixed intervals of times. What is 
true of these parts of the system, is true also of all the parts and divisions of the 
system, because that degree of velocity is assigned to each, by which, in the 
great system of periods, every part preserves forever its normal relation of in- 
ter-position. The Kepler law is not therefore as a sporadic case of disease, 
but one phase or exhibition of the regulated, healthy, and all-pervading order 


of nature. There is, clearly, one relation between the subdivisions of the orbit 
and those of the earth ; and if one part of the earth is thus in correlation with 
an astronomical element, so are all its parts, subdivisions, and individual enti- 
ties. There cannot possibly be a mistake in declaring that a relation of these 
parts exists. The only mistake must be that of the character of the rela- 
tion assigned ; and here, a possibility of error hardly exists, because the 
assigned character is logically deduced from general principles, and the value 
of the divisions of the earth (thus deduced from the character of the rela- 
tion) is responded to by the measured extents of the earth's surface divisions. 

The case could be safely rested here ; but the principle involved is so far per- 
vading, and this extension of it to the terrestrial masses is so far in advance 
of received opinions upon the subject, that proof upon proof and illustration 
upon illustration will be rightly demanded before assent is given. And if the 
doctrine be sound this reiteration of proof and fullness of illustration can be 
furnished : because, a deeply inwrought principle will not peer out, incidentally, 
at wide intervals, here and there ; itwillnotbe seen from the figure of the 
earth, and from the extent of the terrestrial masses only; it will manifest itself 
from every part and division of the globe. 

The Magnetic Equator : By observation this dividing circle of the earth 
is placed at an angle of 19° 47' with the geographic equator. This identical 
position as empirically given, is theoretically calculable upon the principle under 
discussion by use of the measure of the terrestrial masses, (138°), as the datum 
or intermediate term, (p. 90). Consequently, this measure of earth- structure 
is, by the converse process, easily and readily calculable from the location of 
the magnetic equation by observation. 

The Distance of the Sun and of the Moon from the Earth : The difference 
of longitude between the intersections of the tropics by the magnetic equator (at 
19° 47' angle with the geographic equator,) to wit 130°, contains as many times 
the excess of the equatorial regions as the mean distance of the moon from the 
earth contains the moon's diameter ; and as many times as the mean distance 
of the sun from the earth contains the sun's diameter. Thus by the measure 
of the extent of the terrestrial masses, and the angle of the magnetic equator. 
the distance of the sun or moon from the earth can be calculated, (p. 89). 

Other Measures or Boundaries of the Terrestrial Masses : The measures of 
the terrestrial masses of 84°, 42°, and the angle of 30° with the meridian as 
the normal trend of the coasts and the direction of the bearing of world-wide 
distant capes and islands, have been determined from the measure of 13S J . 
(p. 9, 92 and map). These lines and this angle of coasts cover the surface of 
the globe with a net-work of symmetrical divisions. 


There exists, it is true, many exceptions to the detailed system of the ar- 
rangement of the terrestrial masses. These extents of land often fail to reach, 
and often pass beyond the normal measure ; and the trends of the coasts are 
far from being always preserved at the normal angle with the meridian. These 
exceptions are not however infractions of law, but the seeming irregularity is 
another phase of the law of earth-structure. Seismic action, — the volcanoe and 
earthquake, — as apparent earth convulsions, very generally, if not altogether, 
occurs, only where the normal line of the coasts, or the normal extents of the 
terrestrial masses have not been attained. It would seem as if the earthquake 
in its throe is a struggle against an oppressive weight which had sunk the sur- 
face below its normal level ; and that the volcano's blaze is a signal light of 
distress at an incroachment of the ocean upon the coast. Nevertheless, in the 
whole range of the investigation there is no proof of the relation of the struc- 
ture of the earth to the structure of the heavens, which is so clear, and so full, 
and so interesting as the proof from these apparent convulsions of nature. 
The earth's surface-divisions are traced out to be in especial relation with both 
the obliquity of the ecliptic and the ellipticity of the earth's orbit, (p. 49). 
These astronomical elements have changes of value. They oscillate in secular 
periods around a fixed mean. How marked then, the coincidence, how clearly 
these celestial mutations, — these oscillations of astronomical elements, — descend 
to the earth which A created in the image of the heavens ! There is change 
above and the earth's surface is not of one stagnant level nor of monotonous 
repose. ( Section 5, p. 55 et seq.) . Besides, the upheaving force of continents 
is traced to the revolution of the ellipticity of the earth's figure which revolves 
in accord and harmony with the revolution of the ellipticity of the orbit; 
geologically therefore the general positions of the Essay are demonstrated to 
be sound, (Section 7). 

The Distance of the Earth from the Sun as calculated from the measure of 
the terrestrial Masses : From the extent of the terrestrial masses, — that is from 
the maximum distances measured across continuous land, or across an un- 
broken expanse of ocean, — the mean distance of the sun from the earth has been 
correctly calculated by a simple arithmetical process. The surface-structure 
of the earth thus reflects back a light upon the long extent of space which 
stretches itself from this globe to the central luminary, the sun, (p. 95). 

Once more : the distance between the tropics is an astronomical division 
of the earth, and the fraction of a day in one year over 365 whole days is a 
period measured by the axial rotation of 0.242 arc of the earth's circumference ; 
from these values also, the mean distance of the sun from the earth has been 
calculated, giving, in the result, the same value to this "fundamental element 


of the solar system" as before produced. Conversely, from tlie distance of 
the sun and the fraction of a day in a year, the distance between the tropics or 
value of the obliquity of the ecliptic can be calculated, (p. 93). 

By more than fifty differing methods and processes the mean distance of 
the sun from the earth has been calculated from periods, or from other dis- 
tances through the intervention of periods, — the periods being used as interme- 
diate terms or data of the calculations. The results, all of them, agree in 
value, giving also the very value to the distance which is obtained by the one 
process of measurement, — that of finding the sun's parallax ; many of these 
methods are detailed in Section 10 of the Essay, and others will be elsewhere 
found scattered through the pages of the work. 

Nor is this all : On the foundation-principle set forth each and every one 
of the astronomical elements of the sub-system of the sun, the earth and the 
moon has been calculated from the other associated elements of these spheres, 
(Section 9) ; and it is clear that what is true of the elements of this sub-divis- 
ion of spheres must needs be true of the elements of all the spheres of the sys- 
tem ; because, God has no need of special legislation for individual worlds nor 
for individual groups of worlds. 

The Subdivision of Forms and their Structural Affinity : The relative veloci- 
ties and magnitudes of the spheres of the solar system are determined, of course, 
by planetary law ; and, it is averred that the spheres themselves are subdivided, 
and that their subdivisions have, to some degree, an independent existence and 
motion ; and further, that these divisions, as sub -individuals or sub-entities, 
have their magnitudes or extents in harmonious relations among themselves ; 
and that their separate existence, independent motions, and relative extents are 
determined by planetary laws, — the same principles of construction applying 
both to the spheres and to the individual parts into which the spheres are di- 
vided, (p. 81 et seq.) . 

The sun in magnitude is 109.6 times greater than the earth. The redun- 
dancy of the earth's equatorial regions is a division or sub-entity of the earth. 
Therefore, as 109.6 times the earth is the extent of a sphere of the system, so 
109.6 times the redundancy of the earth's equatorial circumference constitutes 
the extent of a sub- entity bearing the same ratio to the redundancy which the 
sun bears to the earth : 109.6 times 82.47 miles is an analogue of the sun to 
the sub-entities, lower than the integral spheres. This logical deduction from 
the doctrine is responded to by the stubborn facts of measurement : 109.6 times 
the excess of the earth's equatorial regions in circumference plus T ' T of it equals 
365.24 times the redundancy of the earth's equatorial regions in diameter 


(26.227 miles) ; and the sun's circumference plus T V of it equals 365.24 times 
the diameter of the earth. The question thus is settled, but this is a part only 
of the support of our sound doctrine given to it by an accurate measure of ex- 
istino- values of extent. 

109.6 times 82.47, the redundancy of the equator in circumference, less T ' T 
of it is equal to the diameter of the earth plus T \ of it. The sun's diameter less 
T ! T of it, as the integer of measure, is contained in the sun's distance from the 
earth 116.2 times ; 116 x 3.1416 = 365.24 which is the number of the days of 
the year. And again : t l of the daily velocity of the earth in its orbit around 
the sun is equal to the daily velocity of the sun's equator in axial rotation less 
T y of it. (See note at the end of this Dissertation.) 

The fundamental ratio of the astronomical elements of the earth, to wit, 
1 to 16, is discussed in Section 11 ; its origin or derivative basis ( p. 90 et seq.) 
is the earth's distance from the sun ; for illustration of its origin : this distance, 
as expressed in sun-diameters, 109.6, multiplied by the ratio of the circumfer- 
ence of a circle to its diameter plus one sixteenth is (3.1459 + T ] -g- = ), say 3.33 +, 
gives in the product the number of the days in one year. The square root of 
"5".tVtt2 °f the distance of each planet ( expressed in sun-diameters) in its ratio 
to the ratio of the circumference of a circle to its diameter, gives to each planet 
-its fundamental ratio or its ratio analogous to the ratio of 1 to 16 in the case 
of the earth, (Method 7, of Section 10) ; and, as the earth's fundamental ratio 
gives the relation of its astronomical elements to each other so the special 
analogous ratios of all the planets give the relation of their respective indi- 
vidual astronomical elements to each other. 

As one important application of the ratio, 1 to 16, of the astronomical ele- 
ments of the earth, the number of the lunations, and also the number of days, 
in one year, will be calculated by it from the mean distance of the earth from 
the sun with no other data than that of the value of the earth's diameter and 
that of the value of the radius of the moon's mean orbit around the earth. 

The science of astronomy as it is now understood and taught in the school, 
confessedly, does not include a law for the determination of the value of the 
year, or of the day, or of the lunation ; nor do its theories show the relation of 
their values to the values of other astronomical elements, — astronomers acknowl- 
edging their ignorance in this important phase of the science. On the other 
hand, in the presented system, this numberof days and this number of lunations 
in a year are shown to be what they are observed to be, because of the values of 
associated astronomical elements, — exhibiting the unity of the system, thus: 

The radius of the moon's orbit around the earth (237,319) is contained in 


the radius of the earth's and moon's mean common orbit around the sun 
(95,375,000 miles) 401.86 times: 401.86 + 16 (the ratio) = 25.115 ; 25.115 — 
0.376 = 24.739, one half of which, 12.369, is the number of the lunations in 
one year, correct to the thousandth decimal. 

The number of the mean diameters of the earth, (7,924) contained in the 
distance of the earth from the sun (95,375,000 miles) is 12,037; 12,037^16 
(the ratio) 752.30 ; 752.30 — 21.82 = 730.48, one half of which, 365.24, is the 
number of the days in one year, also correct to the thousandth decimal. 

In this latter calculation there is deducted 21.82, in the former, 0.376 of 
the integers of measure repectively used. Thus, while the results of the two 
processes are fractionally correct, these processes are identically the same ex- 
cept (as noted) in the two deductions (21.82 and 0.376) which are not jpro rata. 

The deduction of 21.82 is 21.82 times 16 x 7.924, which is equal to 
(21.82 x 7,924 == 172,901 ; 172,901 x 16 =) 2,766,416 miles ; deduct the sum 
of the earth's circumference, 24,881, and the moon's, 6,789, (=31,670) and the 
remainder, 2,734,746 miles, is the value of the circumference of the sun 
(2,733,672 miles), with a variation of (2,734,746 — 2,733,672 =- ) 1,074 miles 
only from its true value. 

In the other calculation there is deducted 0.376 of the integer of the meas- 
ure of 237.319 miles 1 , which is the radius of the moon's orbit around r t the earth. 
The deduction is equal to (0.376x237,319 =89,131 miles; 89,231x16=) 
1,427,709 miles ; an addition to this of T ] T makes a sum of 1,516,940 ; from this 
(1,516,940) deduct *he value of the earth's circumference (24,881) and there 
remains 1,492,059 miles, which is the value of the moon's orbit around the 
earth, (1,491,700) with a variation of 359 miles only. How slight appears 
the discrepancy of the results of both processes with the results of observation, 
when the number and extents of the elements of the calculation are considered ! 
And, calculating from the well measured periods, how exactly, to a point 
almost, can the unmeasurable distance of the sun be attained ! 

It is then a fact of relationship that T \ of the earth's mean distance from 
the sun, measured in earth-diameters, is twice the number of the days of the 
year ; and that T V of the distance of the earth from the sun measured in the 
radii of the moon's orbit around the earth is twice the number of lunations in 
a year, — varying in the first case by the sum of the values of the circumferen- 
ces of the sun, earth, and moon, and in the latter case by the ratio 1 to 16 and 
by the sum of the values of the moon's orbit and the circumference of the earth. 
And conversely, from the number of the clays or of the lunations in one year, 
with the ratio of 1 to 16, the mean distance of the earth from the sun is calcu- 


lable. The number of lunations in one year is thus proved to be in relation 
with the number of days in one year as both are calculable from the same 
planetary elements. 

There is a connected harmony which should be here presented : The frac- 
tion of a day in a tropical or natural year over the 365 whole days is 0.242 +. 
The same law which determines the periods of the day and year relatively to 
each other, of course, gives to this fraction its value. The existence of this fact 
of relationship is thus demonstrated : The fraction becomes unity or, in its 
repetition, is one day in 4.11 years (0.242 + 4.11 + = 1) . Now 365.24 times the 
annual equatorial axial velocity of the earth, to wit, 365.24 times its circum- 
ference, multiplied by 4.11 gives in its product, multiplied by 16, a product equal 
to the value of the earth's orbit ; and consequently the mean distance of the 
earth from the sun, or radius of the orbit of the earth, is readily calculated to 
be 95,375,000 miles, as in more than fifty other processes. It will appear to 
some almost incredible, that the mean distance of the earth from the sun, for 
the attainment of the value of which " astronomers have encountered dangers, 
journeys, suffering, and almost martyrdom itself" (p. 64 & 65), should be thus 
as accurately and readily attained as any other astronomical element of the 
system. Yet so is it. All the astronomical elements of the sun, of the earth, 
and of the moon have been shown to be parts of a perfectly symmetrical 
whole ; 

"And that unto all 

He hath laid out one perfect level law, — 
His will", 

so that from the great distance which stretches itself between the sun and the 
earth, — and from the period, immensely long, in which the perihelion of the 
earth's orbit completes ..a revolution in space, down to a distance across 
an ocean, land to land, on the earth's surface, and down to a period of a few 
hours, constituting the fraction of a day in a year, all other extents of space 
and all other durations of time can be calculated. 

Nor is this to be doubted because that out of hundreds of calculations there 
may be some which are erroneous. How low is the order of that man's intellect 
who would select instances of error in the application of principles and parade 
these errors as a good and sufficient reason to ignore the whole subject! If 
most of the arithmetical illustrations were erroneous — nay, if all were failures, 
the Grod-ordained principles of harmony stand forever, undimmed by error and 
recognized to exist over and beyond all mathematical logic. The sun shines 
to those who cannot describe the beauty of a sun-illumined earth ; the defects 


of description do not disprove its glory nor detract from the joy which the 
beams of the sun throw over a happy world intensely tinted by the light 
from above.* 

To convince the reader of the truth of the extension of the foundation - 
principle there were required many proofs and much illustration. They are 
given ; but, to minds of a certain character, this abundance of illustration and 
this re-iteration of proof will be an obstacle to faith in the doctrine of the Essay J 
'so much' it will be said, 'is claimed to be done, that the author must be a 
visionary and not a pains-taking practical investigator of nature whom it is 
safe to follow.' 

This is, perhaps, sound reasoning, but it is a deduction from false premises. 
There has not been one new idea evolved and not one new theory has been set 
up. A foundation-principle, which, as an abstraction, every one admits, has 
been 'practically admitted and relied upon ; by which working faith very much 
has been accomplished. A feeble light on a bit of steel-wire gives guidance 
to the mariner over the pathless ocean : so, the polarity of the universe, 
although faintly discerned, but trusted in, has guided the investigator in his 
voyage of discovery over the otherwise trackless sea of space. 

Physical science (general physics) in its frequented range of investigation 
makes toilsome and painful progress. Its steps are thus feeble and halting as 
science then walks in the darkest path of investigation. Its subject then is the 
examination of physical causes ; it seeks to know what they are, and how they 
act in the production and continuance of the system of worlds. Science strug- 
gles and struggles almost in vain to discover this, and in what manner, and 
by what processes, and with what virtue the mutual action and re-action of its 

* In re-examining the calculations of the Essay, there appears (page 60, line 21) an error 
of taking the value of the annual precession, (50.18") as the datum of the calculation, in place of 
the linear value of the earth's circumference in arc of its orbit (53.95"). On page 72 there arc 
typographical errors,— the 13th line of this page should read: ■— = l ^~- = s ^~^ . 
On page 93, line 4, the numerator of the fraction, ^£*2 JV - should have been explained to be 7 > s of 
8,433 miles. Other errors of this nature probably exist undiscovered by the author; and, under 
the circumstances attending the publication, there must needs be many other typographical and 
clerical errors, of which those discovered are not noted as they are not of that character which 
prevents a reader from understanding the ideas which the author intends to convey. As instances 
of these : on the 15th page the converse wrong directions arc given to the rivers Obe and Indaa 
(ot Asia) ; and the river, Obe, is spoken of as running into the Indian, when it empties in the 
Arctic ocean, 


parts, the system of things is produced and maintained. This knowledge,^- 
beyond perhaps, a mere smattering, — pertains to the Creator alone. 

The author has no inclination and no reason whatever to deny the action 
of physical causes. Let them be admitted in their full number and in the dis- 
charge of all the functions assigned to them ; allow that they act according to 
the received ideas and that their practical use is to the full degree which is 
claimed ; magnify the importance of their discovery and glorify them to any 
extent whatever. Nevertheless, they constitute the means but not the end; 
they are processes, modes of construction, the tools and implements, but not the 
structure, — not the completed edifice which presents itself in its glory of per- 
fection and in its beauty of simplicity and faultless harmony, (p. 79 et seq.). 
To derive a lesson from the very minute : a diamond in its perfect symmetry 
of form, and in its intense splendor, as if the rays of light loved to linger on its 
faces and around its angles, makes its impression as a complete and perfect 
whole, without the least reference to its constituent chemical elements or to the 
processes and physical causes of its construction and crystallisation. So above all 
processes, and beyond the action of each and every physical cause, the glorious 
Edifice of Worlds presents itself for examination ; and as such it makes its 
strongest and most definite and useful impression on the mind, not of unculti- 
vated man only, but on the universal mind ; and, to see it as such is the best 
preparation for the examination of the parts of which it is composed. The 
laws for the whole and for the parts are one and indivisible ; and these laws 
are most clearly seen in their extended application. Thus, general views give 
to the student of the minor divisions of nature a definiteness of idea. It is 
difficult -to rise to the heavens on facts piled upon facts but light from the 
heavens will bring these facts into more distinct vision. 

The subject of the Essay is vast, and an approach, even, to its perfect treats 
ment requires a great extent of knowledge and an intellectual power of much 
breadth. Therefore, faults must be very numerous ; and yet because the author 
ardently loves nature and has honestly sought the truth this little work cannot 
have been written altogether in vain. And there must be strength in the Essay 
independent of the degree of the qualifications of its author ; because, so great 
and glorious is the thought of the Completeness and Unity 'of the creation, 
based on the attributes of God, that its feeble portraiture has strength and 
must appeal somewhat to the highest and the noblest sentiments of human 
nature. Think of it for one moment: it is a creation into which nothing in 
the least degree capricious or accidental has ever entered ;— a completely sym- 
metrical creation, the most minute parts of which, meted out and bounded, and 


-having their forms and their associated periods in the most perfect harmony with 
the parts and their periods created on the most enlarged scale of expansion, — 
a regulated gradation separating the parts and indivdual entities down to ex- 
treme minuteness, — assigning to each its place and its function, yet bestowing 
upon all, correlations so perfect that not one of the smallest parts could be taken 
away without consequent disorder entering into and defiling the whole system. 
Such in God's truth is it ; and as such the system can be learned, as such it 
should be taught, as the incarnation of God's power and wisdom in the mate- 
rial ; that He, the Creator, may become known, loved and worshipped. Let 
these closing expressions be regarded as the words of an enthusiast, — it mat- 
ters not, for poorly that student of nature has been rewarded whose contem- 
plations of the creation never has caused the heart to glow and the cheek to 
flush by an intense admiration and delight ; and morbidly constituted is the 
man who, with such feelings warm at his heart, does not dare to give to them 
utterance in words. 


The Earth's orbit in relation to the magnitudes of the Earth and Sun : The 
orbit of the Earth, its magnitude as a sphere and the magnitude of the sun as 
a sphere differ widely in extent. Yet, by a special velocity assigned to the 
earth's orbital motion, and by a special velocity assigned to the orbits of the 
axial rotation of the earth and sun, these varying entities become the har- 
monious parts of a perfect sub-system of worlds. 

For illustration of this idea : The natural or tropical year does not end 
with the end of a day ; after the earth has turned around in axial rotation 365 
times it turns 0.242 of a day or of its circumference before the tropical year 
is completed. In 4.11 + years this fraction of a day becomes unity or one day 
by the repetition of the fraction, 0.242 + x 4.11 + = one. Now, the earth's 
circumference repeated 4.11 + times is (24,936 x4.11=) 102,494, and add 
the ratio, T ' T , (6,406) and the sum is 108,900 miles, which is exactly the daily 
axial equatorial velocity of the sun ; — that is, a velocity in this case is assigned 
to the sun so that it is brought into correlation with the earth's circumference 
by the common ratios of 1 to 4.11 and 1 to 16. 

Again, the sun rotates or turns on its axis 14.48 + times in one year, and. 
as its circumference is 2,733,739 the annual equatorial axial velocity of the 


sun (14.48 + times its circumference) is 39,784.000 miles. The annual equa- 
torial axial velocity of the Earth (365.24 times its circumference) is 9,108,000, 
4.11 + times of which is 37,450,000; add thereto (as before) T \, 2,338,000 the 
sum is 39,784,000 ; and as the annual axial velocity of the sun is 39,784,000 
miles, the same relation is exhibited as before. The annual axial velocities of 
the sun and earth therefore have the same ratio to each other as the daily velo- 
city of the sun to the earth's circumference. (See p. xvin.) 

It is evident therefore that the special degree of the orbital velocity of the 
earth the special degree of the axial velocity of the earth and of the axial 
velocity of the sun were assigned to the varying extents of the orbit and of the 
circumferences of the two spheres in that degree to each by which in common 
ratios they become equal. 

There are many other elements of the sun and earth and elements of the 
moon which are brought into concomitaney or equality by the application of 
the same ratios. For which the reader is referred to the Essay. (See, 
especially, p. 83.) 

One other view of these harmonies is reserved for special and separate 
consideration : to wit, -j\ of the number of earth- circumferences which is con- 
tained in the mean distance of the earth from the sun, (12,037 -^ 16 == 752.30) 
is twice the number of the days in one year plus 21.82. (21.82, as shown, rep- 
resents or answers to the sum of the sun's, the earth's and the moon's circum- 
ference, see p. xvii of preceding: ) In harmony there are contained in the 
diameter of the earth's orbit (219.24 x 3.1416 =) 219.24, and of course in the 
circumference of the orbit 689- times the sun's diameter ; add to this r \ of 
it (say 41 + ) and the sum is, 730, which is also twice the number of the days in 
the year. Thus, to found or determine the value of the orbit both on the mag- 
nitude of the sun and on the magnitude of the earth; and to make the day a 
harmonious period in the system of periods, the ratio 1 to 16 is introduced ; 
and, further, to bring into harmonious relations the axial velocities of the 
earth and the sun, the ratio of 1 to 4.11 is introduced. Thus, the otherwise 
conflicting values of periods and of extents or " distances" of the divisions of 
the system are reduced into harmonious relation. And, once further ; it is 
believed, (and this, not without strong reasons for the faith), that on the pre- 
sented system all the astronomical elements of all the spheres of the solar sys- 
tem can be calculated with perfect and reliable precision, — the eye of the mind 
penetrating space to depths to which the sight of the telescope can never 
reach ;— and this, because of the perfection and of the simplicity with which, 
the Divine Architect has constructed this Edifice of Worlds. 




It is said that " the planetary system, in its relations of absolute magni- 
tude, relative position of the axes of rotation, and density, has, to our conception, 
nothing more of actual necessity than the distribution of land and water on 
the surface of our globe, the configuration of continents or the elevation of 
mountain chains." 

Humboldt, in writing thus, could not mean that either these astronomical 
elements or these telluric phenomena are accidental or fortuitous. They are so 
" to our conception." The law which determines certain astronomical values 
and the configurations of the earth's surface- divisions is not known : no rationale 
has been assigned ; their relations to the other parts of the creation have not 
been traced out. Thus there are two classes of facts, to wit: the apparently 
fortuitous or chance-coincidences, and those for which the science of the day is 
able to give the rationale and relations. 

The facts of the telluric phenomena (configuration of continents, &c.) are 
placed under the fortuitous class, and are considered as of paroxysmal origin. 
They have "arisen (according to Humboldt and to generally received science) 
out of the conflict of forces acting under unknown conditions." Prof. J. P. 
Nichol says, (System of the World, p. 171,) "If we interrogate the existing 
configuration of the earth's surface, we have no choice but to consider it the 
offspring of the wildest caprice." De Beaumont says, on the other hand, 
(System of Mountains) that "the distribution of mountains is not at random 
(au hazard) as is the distribution of the stars:" that is, he had a system for the 
position of the mountains, and none for the position of the stars. 

As science advances, these facts of earth configuration will be reclaimed 
from the fortuitous class, and united with those phenomena for which a law can 
be assigned. 

There is a oneness of style in the works of nature. Form is linked into 

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form, — every form gliding gently into other analogous forms, the derivatives 
retaining the character of the generating type as fully as their positions and func- 
tions will admit. As a beautiful instance of this, a leaf declares the form of 
the tree on which it grew. Its petiole, or footstalk, is an analogue of the trunk 
of the tree, being comparatively long or short as is the trunk of the tree from 
the ground to the point of the offset of its first branches. The veins of the leaf, 
as they extend from the centre or midrib vein, shoot out at the same angle as 
shoot out the branches from the stem of the tree ; and the veins are whirled, 
reticulated or otherwise distributed as are the branches. A leaf thus gives a 
miniature drawing of its parent tree : it writes down on its tiny page the cha- 
racter of the great vegetable organization of which it is a minute appendage. 
This fact was established in the examination of one hundred and ten species. 

This repetition of structure is not confined to organic formations ; for instance, 
the contour of continents is repeated in islands. Nor is the repetition of form 
limited to parts of the earth, the orbit of revolution around the sun has at least 
one of its characteristics (its ellipticity) repeated in the ellipticity of the figure 
of the earth, which gives the form of the orbits of axial rotation. So the angle 
of the earth's axis with the ecliptic has its value repeated, under a modifica- 
tion, in the angle of the trend of the coasts, as will be after set forth. 

One step has already been taken, by Professor Owen, in unfolding the rela- 
tions between astral and telluric phenomena. He announced that, if a terres- 
trial globe has its north pole elevated 23° 28', which is the value of the obli- 
quity of the ecliptic, the horizon of the globe will be in line with the trend of 
the coasts of one side; and if the pole be depressed 23° 28', the horizon will 
mark the trend of the coasts of the other side of the continents. 

This coincidence has been attributed to the influence of the sun on the 
cooling and solidifying of the earth's crust, which is considered as having been 
once fluid by heat. 

An original fluid earth, consisting of melted lava, which gradually cooled, 
forming the earth's crust, is taught by the science of the day. It is difficult 
for the geologists to give up this hypothesis ; for it appears to them to be neces- 
sary, to account for the elliptical figure of the world, for the existence of 
trachytic or igneous rocks, for earthquake and volcanic phenomena, for the 
elevation and depression of earth-level, and for the inclinations, disruptions, 
and distortions of earth-strata ; all these geological phenomena being ascribed (in 
the phrase of Humboldt) "to the reaction of the interior on the surface of the 
globe ;" and until this " reaction" is given up, as a cause, the hypothetical fiery 
furnace within the earth will be preserved, to supply the sufficient force. The 



original fluid earth served also to account for the " coincidence" brought to light 
by Professor Owen. In stead of tracing it to astral phenomena, this idea was 
buried in the fluid nucleus of the earth. 

This looking down into the earth, below its surface, for a cause of the 
surface telluric phenomena, has diverted the attention of science, and turned it- 
aside from what is to be presented as the true path of investigation. 

These preliminary statements are made in order to indicate the course 
of thought which led to the results herein to be set forth. This essay 
neither upholds nor denies the existing hypotheses. It deals with facts. It 
is intended to bring to light certain phenomena which exhibit the symmetrical 
arrangement of the earth's surface, and certain facts which point to the relation 
of the structure of the earth to its planetary elements. 

The symmetry of the surface structure of the world has not been altogether 
overlooked by science. Bacon long ago pointed out the triangular shape of the 
continents ; and he regarded this instance of symmetry as opening a path to a 
more extended knowledge of earth-structure. Reinhold Foster developed some 
other instances of the symmetrical structure of the globe, showing that the 
southern terminations of the continents are high and rocky, and have east- 
ward an island or a group of islands ; and that the western coasts have deep 
bends or concavities. Humboldt pointed out the salient angles of the Alantic 
coast of North and South America, and the re-entering angles of the opposite 
(west) coast of Europe and Africa. Stiffens extended the symmetrical contour 
of continents to islands and peninsulas, showing that Greenland,' California 
and Florida, in America; Scandinavia, Spain and Italy, in Europe; the two 
Indias, Corea and Kamtchatka, in Asia, resemble the continents in contour, 
each being triangular, with a sharp angle to the southward. Ritter first showed 
that the globe can be divided into two hemispheres, the one being the land or 
continental hemisphere, and the other, the water or oceanic hemisphere. For 
these principal and some other such facts of symmetry the reader is referred 
to the "Cosmos" of Humboldt, and to M. Gruyot's "Earth and Man." 

So much uniformity has been brought to light, and so many analogous 
earth-divisions are apparent, that, in the language of Sir Charles Lyell, "no 
invention of a cataclysm or series of paroxysmal waves can avail us."* The 
known analogies thus set forth are, however, far— very far from completing the 

*In fact, it is geology which, by its discoveries of earth-structure, first indicated the existence 
of an equable, widely-extended and uniform action of the upheaving force of the continents, the 
result of which must necessarily be the symmetrical contour of the earth's surfa -e-divisions. 


harmonious relations of the masses of land and areas of water, the symmetry 
of their breadths and lengths, the one direction of the trend of the coasts, and 
the one bearing of distant capes, headlands, bays and other angles of contour. 
The position now taken, and which it is the object of this essay to support, 
is, that every mass of land and every area of water, in relative position, in 
dimension, and in figure, or contour, is placed and constituted under a law 
which gives also the figure of the earth as a sphere: or, in other words, that, as 
the structure of the earth, as a whole, is normal, so its parts, as surface-divis- 
ions, have normal limits and determinate forms, and are symmetrical parts of 
a symmetrical whole. 

Description of the Map. 

On a map on Mercator's projection the degrees of longitude are made equal, 
while in nature, or on a terrestrial globe, these degrees lessen north and south 
from 69.27 miles, for a degree on the equator, to nil at the two poles. This 
equality in the degrees of longitude does not distort the bearing of places 
from each other, inasmuch as the error is eliminated by the Mercator-map's 
having its degrees of latitude increased from the equator to the poles, when on 
the sphere or globe these degrees of latitude are equal. 

Certain east and west lines are drawn on the accompanying map, marking 
the distances of earth-surface points from each other. These distances will 
be called cognate distances, being equal arcs of axial rotation in equal times: 
for the law which determines east and west distances, or breadths, reduces cog- 
nate (or equivalent) distances as the degrees of longitude are reduced on the 
sphere from the equator to the poles. On a Mercator-map, the degrees of longi- 
tude not being reduced, cognate distances show themselves by their equality of 
length or arc. 



The Major [North and South) and the Minor (East and West) Axes of the Conti- 
nent, and the Bearing, or Trend, of their Coasts. 

Attention is first to be directed to the north and south dividing lines, 
or meridians. These are 90° longitude apart; and thus they divide the world 
into four equal longitudinal sections. 

The first meridian line is the major (north and south) axis of the conti- 
nent of America, in 70° west longitude; the second, 90° cast of the former, that 
of Europe and Africa; the third, 90° east of the last named, is that of Asia; 
and the fourth, still 90° further east, is that of the Pacific ocean ; and it is, 
hypothetically, the major axis of a continent once existing, but which has sub- 
sided beneath the ocean. 

These north and south axes extend 138°; that is, from 542 ° south to 83i° 
north latitude ;* and it will be perceived that Europe and Africa are considered 
as forming one continent, or one natural division of land,f apart from the con- 
tinent of Asia. 

The land of the continent of America actually terminates at Cape Horn, 
in 54i° south latitude, while Europe-Africa, and also Asia, have, hypotheti- 
cally, their terminations of relief in the same parallel, to wit, 54* °. 

The correctness of this symmetry, or equality, of the southern termina- 
tions will be made apparent. But it may be well to state, in this connection, 
that the termination of the dry land of continents may be only the termina- 
tion of the visible relief of the continent. There may be, and often is, a contin- 
uation of a relative greater height of the basin of the sea concealed under 
the water. 

*The greatest stretch of land, north and south, is that of America. The land from Cape 
Horn, say in 54° 30' south latitude, rises to 83° 30' north latitude. The distance is 138°=9G00 
miles (G9.27 miles to one degree). A mile, as used in this essay, is y-^jy of the earth's equatorial 
diameter. Beyond 83° 30' there is the open Polar ocean. 

f Steffins combines Europe with Africa. M. Guyot says, the features of relief sever Asia into 
two parts, adding that eastern Asia forms a continent by itself. It will be after clearly shown 
that Europe and Africa should be taken as one mass of land, as North and South America consti- 
tute one continent. 



As a general law, where the terminations of dry land are mountainous the 
oceans are deep near the coast; shallow seas, however, are found south of the 
lofty terminations of Africa and Asia. The seas which bathe southern China 
scarce any where reach the depth of three hundred feet, — the depth of ocean 
beginning east of the Indian Archipelago. The massive point of the south of 
Africa (Cape of Good Hope) ends with very abrupt coasts, and yet one hundred 
miles further south there is only six hundred feet of water.* 

The discussion of these major (north and south) axes of length will now be 
suspended, in order to present the minor (east and west) axes, or axes of the 
breadth of the continents. v 

Under the north tropic the major axis of Europe- Africa divides Africa- 
Arabia into equal breadths. f There is a distance of 42° arc on each side of 
this north and south axis, or of 84° arc from ocean to ocean. Also, from the 
major axis of America, on the north tropic, westward to the Pacific ocean, is 42° 
arc; and from the major axis of Asia (also under the north tropic) westward 
over land, from ocean to ocean, is 42° arc. This 42° arc is the semi-minor axis 
of breadth (east and west), 84° arc being the minor axis of breadth. 

Rhumb lines are arcs of great circles of the earth angularly intersecting 
the meridian lines. All these diagonal lines, drawn on the map, are at the 
same angle, to wit, thirty degrees. 

Let one of these diagonal lines be examined — the one which is drawn from 
the actual southern termination of South America, rising north-eastward: it 
will be seen that this line, with very great, if not perfect exactness, marks the 
mean trend of the south-east coast of South America, and also the trend of the 
north-west coasts of Africa and Europe.J 

There have now been presented three values or measures : the first, 138° 
arc, as the major axis of length (69° semi-axis of length); the second, 84°, as 
the minor axis, axis of breadth (42° semi-axis); and the third, the angle 30°, 
as giving the trend of the coasts. 

These values may be regarded as found empirically, that is, as derived 
from actual measurements. 

* Guyot's Earth and Man. 

■j- Geologically, and in physical geography, Africa and Arabia form one mass of land. Arabia 
is said by eminent geologists to have been disrupted from Africa in the Jurassic Era. In place of 
disruption the relief of the continent may continue across the Red Sea. 

\ The mean trend of a coast is the line beyond which there is the same area of land as there 
is area of water within the line. 


But the value of the trend-line, the angle of thirty degrees and the value 
of the semi-axis of forty-two degrees of arc, are to be obtained trigonomctri- 
cally from the value of the obliquity of the ecliptic (23° 28') , and the rationale 
of this will be after given. 

The triangle ABC (at the south-west corner of the map) has a right 
angle at A; the side AB is made equal to 23° 28' arc; the hypotenuse to 
(twice 23° 28') 46° 56' arc, which is the distance between the tropics ; then the 
side AC is found equal to 42° arc, and the angle at C equal to 30°.* 

It is thus shown to be a fact, that the semi-minor axes of continents, with 
the angle of the trend of coasts, is calculable from the value of the obliquity of 
the ecliptic. 

The minor axis being (42° X 2 =) 84°, then 360° — 84° = 276°, one half 
of which, 138°, is the length of the major axis, and these (84° and 138°) are 
governing values of the dimensions of areas of land and water. 

Before applying these measures, one for pervading symmetry should be 
set forth. The measure of breadths of land is also in many cases the measure 
of the breadths of ocean. The land is above the level of the ocean because of 
its upheaval, and there is ocean because of relative subsidence of land ; and the 
upheaval and subsidence are determined by one law : therefore it follows that 
on the earth, as a whole, its elevations and depressions being harmoniously 
connected, and the level of the waters is so nicely determined that the oceans cover 
breadths equal to breadths which arc left bare of water. Connect this with another 
fact. Trace on or near the magnetic equator a great circle of the earth 19° 47' 
oblique to the geographical equator, the circle commencing on the west coast of 
South America, under the south tropic, and passing to the north tropic at the 
extreme east cape of Arabia, then through the south coast of Asia, and so on : 
the level of the ocean water is so determined that 180° of this circle is land, 
(broken only by a narrow and shallow part of the Atlantic), and 180° is ocean, 
unbroken by land. 

Many islands are off concavities of the coasts of continents, and many 
peninsulas are at the north united to their continents. 

On the south tropic, the island of Madagascar lies off a bay on the cast 
coast of Africa. Consider this island as disrupted and impelled from Africa. 

*The angle (30°) will be produced if the hypothenuse is double of one side, of any value ; 
but the other side will be 42° arc only by values as given from the obliquity of the ecliptic. That 
is, the angle 30° and two sides give one side as 42°. 


It is so far removed to the east that the west coast of the continent and east 
coast of the island are 42° arc apart under the tropic. 

The peninsulas of California (North America) and of Arabia, under the 
north tropic, are northward united to the main land. Now, the points of these 
peninsulas under tropics are moved, the one eastward, the other westward, 
just so far that they are 42° from the major axes of their continents. 

From the peninsula of California look north (see map) on the west Amer- 
ican coast, and a smaller peninsula will be found (say in latitude 52°) resem- 
bling that of California in contour ; from this northern peninsula westward, 
across the Pacific, to the peninsula of Kamtchatka, in Asia, is (twice 42° =) 
84° arc. Both these peninsulas are joined to their continents northward; and 
it is the inclination of their southern points, the one to the east and the 
other to the luest, that makes them 84° arc asunder. The arc 138° is the major 
axis of continents. This is the measure from the west coast of Africa, under 
the north tropic, westward, through Africa, Arabia and Asia, to an island, near 
and off the east coast of Asia. This island (isle Heinan, almost a peninsula,) 
with its distance from Asia, is included in the measurement. There are other 
instances of this symmetry. In the place of disruption the relief between 
peninsula and continent is often continued under water; but the subsidence of 
land under the water-level is regarded as paroxysmal. Thus by what is called 
paroxysmal action the symmetry of the world is actually preserved. 

These facts are important as proving that "the upheaving force" of geology 
is not paroxysmal in its action, and that it acts on the earth normally as a 
whole. Even where cataclysms have been supposed to have thrown masses of 
land asunder, the limit of separation is law-determined. 

There is another fact which indicates the relation of surface-contour. The 
measures, 138° and 84° arc, are specially applicable to earth divisions under 
the tropics. The tropics are astronomical divisions of the earth. 

Let it be supposed that the angle of the trend of the coasts, to wit, 30°, is 
derived from measurement, if thereby the magnitude of the earth can be 
calculated, a symmetrical relation between the earth as a whole and its surface 
divisions will be established. A line (radius) from the earth's centre to the 
equator is, of course, at 30° angle with a line (radius) to the 30° parallel of 
latitude. Make 42° arc the diameter of a circle, on latitude 30°. The value 
of one degree of longitude on the 30 9 parallel is 60. miles; 42° X 60 = 2520; 
2,520 X 3.1416 = 7,920 miles, which is the value of the earth's diameter. 
That is,. 42° arc of longitude at latitude 30° equals the diameter of a circle the 


circumference of which equals the diameter of the earth. This relation, at 
this time, is given as a fact, or accidental coincidence, if the term is preferred, 
the qualifying term, accidental, meaning only that it falls out so, happens to 
be so, is so. The perfect universe is full of these "accidents" of symmetry. 


Discussion of the Major and Minor Axes of the Continents. 

First, the arc 42° under the tropics will be discussed. It has been indicated 
that 42° arc, running east and west from the major axis of Europe-Africa, 
reaches to the ocean on both sides ; that this arc west both of the American 
and Asiatic axes reaches to ocean ; 42° arc is the breadth of South America on 
the tropic, with relief under the ocean ; 42° arc forms the breadth from the 
west coast of South America to the east coast of Madagascar, and it is also the 
breadth of Australia, under the tropic. The arc (twice 42° =) 84° measuring 
the breadth of Africa- Arabia, under the north tropic, measures with equal 
exactness the following ocean-breadths : the Atlantic, under the north tropic ; 
from the west coast of Africa to the east coast of Mexico, across the Atlantic ; 
from the east coast of Africa, westward, across the Atlantic, under south tropic, 
to the eastern shore of the Pacific ; and from the east coast of Africa, under 
this tropic, eastward, to the west coast of Australia. These are all measures 
under the tropics. 

The cognate ocean breadths of 84° arc will now be set forth. The north 
Atlantic, from Iceland to Nova Zembla; from Hudson's Bay (say north lati- 
tude 55°) to Denmark; the south Atlantic, from the west coast of North 
America, eastward, to Africa; from the south-east point of Cape Horn to the 
north and south axes of Europe-Africa; the Pacific ocean, from the west coast 
of South America, westward, near the south tropic, through unbroken ocean, 
to an archipelago, forming the boundary of the subsided area; the Pacific, 
in say north latitude 52°, from the west coast of North America, westward, to 
the east coast of Kamtchatka (Asia), and so on. 


The arc 138° (major axis): From the west coast of Africa, east, to the 
east coast of Australia, is 138°, under the south tropic ; thence to the west coast 
of South America is 138°; and thence there is 84° arc (138 + 138 -j- 84 = 360°) 
to the starting point, being the west coast of Africa. 

Cognate breadths of land of 138° arc: Europe- Asia, say in north latitude 
60°; the breadth, from the waters of the Baltic, eastward, to the Pacific; the 
breadth, from the west of Africa, under the north tropic, west, to an archipelago 
in the Pacific ; and the breadth of North America, from Behrin's Straits to the 
east shore of Greenland. This line (138° -*- 2 =) 69° arc, and gives the latitude 
of the northern coast of Europe and Asia. 

Other repetitions of these measures can be traced out; and if the relief of 
the solid crust of the earth, under water, were visible, many other cognate 
breadths would be brought to view. 

The four major (north and south) continental axes are now the subject of 
discussion. These axes are not empirically located, and yet could be so located 
from the features of the contour of the land over which they pass. 

The American axis commmences south, at the extreme southern cape of 
this continent (Cape Horn). It touches the west coast of South America, 
under the south tropic. It passes north, out of South America, at its extreme 
north cape. It re-enters land of North America at a cape, or headland. It 
then traverses a part of the United States, and across British America, It 
touches an extreme north cape, at the entrance into Baffin's Bay and Hudson's 
Straits, and indicates the mean north and south trend of a coast beyond the 
Arctic Highlands. 

The major axis of Europe-Africa passes from 54s south latitude into the 
extreme south cape of Africa. It divides Africa- Arabia, under the north tropic, 
centrally. Entering the Mediterranean, at its extreme south coast, [it passes 
into the Baltic Sea, also at or near its extreme south coast; it exits from 
Europe at an extreme northern island of the coast; and it enters Spitsbergen 
in the same latitude under which the axis of America enters the "Arctic High- 

The major axis of Asia rises from its southern terminus, in south latitude 
54i°, touches the extreme west cape of Australia, enters the Indian Archipelago 
at its extreme southern island, traverses two of its principal islands, and, 
entering Asia proper, terminates north, at a cape stretching into the Arctic 

The major (north and south) axis of the Pacific Ocean is the fourth and 
last. This, commencing north, near Behrin's Straits, descends south, centrally, 


through the great ocean, and also, centrally, between the east and west spread- 
ing archipelagos of the Pacific. 

According to Professor Dana, the subsided area of the Pacific Ocean has 
its maximum subsidence between the meridians 150° and 180° west (mean 
165°). The major axis of the Pacific is in 160° west. 

The major axis of the Pacific ocean passes over less land (and near to 
more islands) than any other meridian, or north and south line which can be 
drawn through this ocean. It is, as before said, hypothetically the major axis 
of a continent existing in a former geological era (the tertiary?) , and which has 
subsided far beneath the level of the sea.* 

These four major axes have striking and analogous characteristics. They 
are all 90° apart, and those of America, Europe -Africa and Asia pass from 
south into the extreme southern capes of their continent. The major axis of 
America touches the west coast of South America, under the tropic, having 
say 42° arc semi-axis of breadth,f to the east. At the north tropic, from this 
axis westward, to the shore of the Pacific, is 42° arc; from this axis eastward, 
in latitude 69°, to the east coast of Greenland, is 42° arc distant. 

The major axis of Europe- Africa, under the north tropic, divides Africa - 
Arabia into two equal parts, of 42° arc. As before said, the major axis of 
Asia has, from water to water, 42° arc of land, on the tropic, to the westward. 
So of the north and south axis of America. 

All these measurements may not be fractionaly exact, as the elevations of 
land, or relief, may be extended under the water. Some are exact, and the 
others very approximately the true measure. 

The American axis passes over two inland seas, to wit: the Gulf of Mexico 
and the connected Hudson's and Baffin's Bays. The axis of Europe- Africa 
also passes through two seas, to wit: the Mediterranean and Baltic. All these 
three north and south axes pass over more land than any other meridian lines, 
while the fourth, that of the Pacific, passes over less hind than any other 
meridian line, indicating the maximum of subsidence. 

The major axes of America, Europe- Africa and Asia not only pass over 
the greatest north and south stretches of continents, but also over equal, or 

*Each coral island, or atol, is "literally, as well as poetically, a coral urn over a buried 
rocky island," (mountain of a continent). The subsidence is thus a vast area of say 2,000 
miles wide by 6,000 miles long. 

f Taking into view a submarine relief, known to exist : the measure is not accurate, as applied 
to the visible relief. 


nearly equal, lengths of land (excluding water). An examination of the map 
will show that the difference of the north and south visible lengths of the relief 
of the three continents is from the interposition of inland seas. There is not 
one large inland sea in Asia ; therefore this continent is the shortest, north and 
south; and the difference between the north and south lengths of America 
and Europe-Africa is from the greater length (north and south) of the Gulf of 
Mexico and the Hudson-Baffins Bay, compared with the north and south 
lengths of the Mediterranean and Baltic seas, of Europe. 

The three major -axes of America, of Europe- Africa and of Asia pass 
centrally through their continents, north and south ; and the fourth, that of the 
Pacific, centrally through this ocean. 

One other significant fact will be given, as incidental, or without comment: 
the earth has two magnetic axes and four poles, or points of no variation. Two 
of the poles (mean) are coincident with continental major axes. 

It is taught (Gruyot's Earth and Man) that there is a fundamental 
difference in the structure of the new continent and that of the old world; the 
major axis of the former, it is said, runs north and south, and the major axis 
of the latter (across Europe-Asia) runs east and west, 

This anomoly does not exist in nature. The error appears to arise from a 
division of continents, physically, geographically and geologically wrong. 

The normal division of the old world is by a continuation, into Asia-Europe, 
of the line forming the mean trend of the east coast of Africa, This is a 
Rhumb line, at 30° angle with the meridians running from the Cape of Grood 
Hope. (See the map.) This line, dividing Asia proper from Europe proper, 
passes over a plain, unbroken by mountains, "no important ridge sepcirating 
the steples of Ural from the table land of Iran."- The level of some land 
over which this dividing line passes is much lower than the level of the ocean, 
(the region west of the Caspian sea), being the site of a former ocean. 

This dividing line gives to Europe-Africa a contour resembling that of 
America. It also gives Europe-Africa an area equal to the area of North and 
South America, and this division leaves an equal area for Asia. And, if the 
continent, or the relief of the continent, of Asia, under water, were visible, the 
three continents would be of one shape. 

It is stated (Rees' Encyclopedia, Art. Continents) that the areas of land of 
Asia and Australia and that of Europe- Africa (thus divided) are each 2,471,000 

*A chain of mountains (the Ural), running north and south, separates the low part of Europe 
from the low part of Asia. Geologically, Asia proper was once divided by water from Europe. 


square leagues. The area of America (by the same authority) is 2,141,000 
square' leagues. A similar Rhumb line, from La Plata, north-westward, 
(30° angle) equally divides the continent of Worth and South America. La 
Plata (from which this line rises) empties into the Atlantic in the same latitude 
with the Cape of Good Hope, from which the east Rhumb passes north' east, 
equally dividing Europe-Africa from Asia proper.* 

Before the further discussion of the Rhumb lines of the map, attention 
is directed to the meridian lines which divide equally the Atlantic and the 
Indian ocean. 

There is an island, say in south latitude 50° and in east longitude 70°, in 
the Indian ocean (the island of Desolation). A line clue north from this 
island divides the Indian ocean into two equal areas. This meridian line 
enters Asia at the mouth of the Indus, and passes out of the continent, in the 
Indian ocean, at the mouth of the Obe. The Obe is the largest of the Asiatic 
rivers; the Indus is among the largest. (Johnston's Physical Atlas.) The 
Indus runs northward, and the Obe southward, forming the geographical, and 
almost equal, division of Europe and Asia, 

Continue this meridian line north, as the line dividing the north- Atlantic 
from the Arctic ocean ; then the Atlantic ocean (thus bounded east by this 
meridian, which equally divides the Indian ocean) is itself divided by the 
meridian of say 15° west ; and this equally dividing meridian is the only north 
and south line which touches both the new and the old worlds, the new on the 
extreme east cape of Greenland, and the old on the extreme west cape of Africa. 

* According to Captain de Freycinct, the following are the relative linear areas of the 
geographical divisions of land : Asia as 17 ; then America will be 17 ; Africa 12 and Europe 4, 
together 16; Australia 3. — Philosophical Magazine. 



The Trend of the Coasts of the Continents. 

The Rhumb lines become now the subject of discussion. 

These diagonal lines are inclined at an angle of 30° with the meridian 
lines. There are eight of these lines, drawn from the southern termini of the 
four major axes, one on each side. To distinguish them, the line from the 
terminations of the American axis inclining to the west will be called the west 
diagonal of America; the line inclining east, the east diagonal of America. 
So of these lines from the southern terminus of each of the four major axes. 
Thus there will be indicated the axis from which a diagonal rises northward, 
and its direction, whether east or west of north. 

Attention is first directed to the west diagonal of America. This diagr- 
onal rises from the south terminus of the American major axis. It strikes 
North America at Cook's Inlet (north latitude 60°), and it marks the trend of 
the coast south from Cape Lisburne for some four degrees of latitude. This 
line is the normal trend of the western coast of America. In fact, the Pacific 
ocean east of this diagonal is shallow, the ocean-hidden relief of this conti- 
nent extending westward from the visible relief. 

In support of this, M. Gruyot says that, under the parallel of Lima, (South 
America) , forty miles from the coast, the Pacific has only five hundred feet of 
depth, while, on the other hand, the low plains of Bordeaux, (coast of France), 
look out upon a sea the bottom of which sinks, at a very short distance, lower 
than one thousand feet. The east diagonal of America runs near this coast (of 
France), while the shallow waters of the west coast of America reach out to 
the west diagonal of America, which is at a great distance. 

Let it be especially noted that this line, the western diagonal of America, 
strikes cape Lisburne, a prominent cape of America ; thus the calculated angle 
of 30° indicates the bearing of world-wide distant capes. This bearing, stand- 
ing alone, might be deemed an accident (if there were accidents in nature); 
but, with what follows, it must be admitted to be a most significant fact. 

The east diagonal of America, as before said, forms, with very great 
exactness, the mean trend of the south-east coast of South America, and 
also the mean trend of the north-west coast of Africa and of Europe. So far as 


the eye can measure, on a map of large scale, it appears to be exactly the mean 
trend of the coasts. 

By the expression "mean trend" it is meant that there is the same area of 
land on the one side as there is area of water on the other side of this line. An 
inspection of the map shows that this fact exists throughout the whole extent 
of the diagonal.* 

The extreme west cape of Africa and the extreme east cape of South 
America, on the Atlantic, both stretch out and terminate near this diagonal, 
and both capes are at equal distances from it. This diagonal also passes over 
small islands off South America, and over or near Cape de Verde and Canary 

The west diagonal of Europe- Africa rises from the theoretic termination 
of this continent (53i° south latitude), passes north, up the Atlantic, in the 
range of two solitary ocean-islands (St. Helena and Ascension) :\ It crosses 
the equator midway of the Atlantic. Entering America at Labrador, it forms 
the mean trend of the coast south of Baffin's Bay ; and also of the trend of 
other inland seas. 

Let it be here observed that these diagonals not only give the mean trend 
of oceanic coasts, and the bearing of distant oceanic-capes, but also the bear- 
ing of isolated ocean-rocks, and the trend of the coasts of inland seas. Com- 
pare the west of America with the west diagonal of Europe- Africa : the former 
gives the bearing of Cape Lisburne (far north) with the Cape of Good Hope, 
the latter diagonal gives the bearing of the extreme north trend of coasts of ]^orth 
America with the theoretic termination of the relief of Africa at the south. 

The east diagonal of Europe-Africa passes from its southern terminus 
(latitude 53 P south) over the isolated island of Madagascar, over an extensive 
group of small islands, shallow water and sand banks, % enters Asia at the 
meridian equally dividing the Indian ocean, traverses the continent of Asia, 

*This line also truly, or very approximately, divides in equal areas the waters of the Atlan- 
tic, lying between the major axis of America and that of Europe-Africa. 

-\ One is very slightly to the east, the other slightly to the west of the diagonal ; they are 
equidistant from it. The submarine relief of these islands is traversed by the line. 

\\t forms the major axis of length of this island (Madagascar), giving the bearing of its north 
and south capes ; its north cape being slightly to the west, and its south cape equally to the east 
of the line. Compare this with the position of the two islands (St. Helena and Ascension), in 
relative position with the west diagonal of Europe- Africa. Isolated islands and sand-banks are to 
be known, and avoided by navigators, by the use of these diagonals, in unknown pails of ocean. 


and forms the trend of a group of islands of the Arctic ocean. This diagonal 
is parallel to the mean trend line of the east coast of Africa, being the normal 
trend line. 

The west diagonal of Asia rises in latitude 54i° south. It passes up the 
Indian ocean, over small islands, sand banks and shallows, touches the extreme 
east cape of Arabia, and forms the trend of the north-east coast of Arabia. It 
touches the south-west point of the Caspian sea, the north point of the Baltic and 
the west j>oint of a branch of the Baltic; and, leaving Europe, it marks the 
trend of the south-west coast of Spitsbergen. 

The eastern diagonal of Asia runs across Australia, and then passes, par- 
allel to the mean trend line of the coast of Asia, to Behrin's straits, where it 
intersects with the west diagonal of America. After this intersection, the east 
diagonal of Asia forms the trend of the north-west coast of Russian-America. 

The west diagonal of America was first discussed, and this, from its south- 
ern terminus, passes north to Behrin's straits ; and, also, the last discussed 
diagonal, from Asia, eastward, also runs into Behrin's straits. The world has 
been thus passed around with diagonals, leaning alternately to the west 
and east, at 30° angle to meridians from north and south axes which are 90° 

The east and west diagonals from the south terminus of the Pacific major 
(north and south) axis are not required for the circuit. The symmetry of 
surface-structure is complete without the hypothetical subsided continent. 

Nevertheless, there are certain facts which seem to acknowledge this theo- 
retic continent. Its major axis descends from Behrin's straits, at the intersec- 
tion of the two diagonals last spoken of. The east diagonal of the Pacific from 
its north and south axis strikes the extreme south cape of the long peninsula 
of California, on the west coast of North America (cape St. Lucas). It also 
touches the north-east cape of Labrador, and indicates the trend of the south- 
west coast of Prince William's Land (or Cumberland island). The 1 west 
diagonal of the Pacific axis touches a prominent north cape of the east coast 
of Asia, traverses this continent, and forms the trend of a part of the north 
coast of Asia. 

Besides the eight diagonals which have been described, there are other 
lines drawn on the map parallel to them. 

One of these is from the extreme east island, eastward, otf and near Cape 
Horn, which diagonal runs north-eastward, over the Atlantic, and through 
parts of Africa and Europe. This forms the interior mean trend of the north- 
erly coasts of Europe- Africa. The land north-west of this would fill the areas 


of the Mediterranean and Baltic seas, within (east of) the line. It marks also 
the trend of portions of the coasts of these inland seas. 

A diagonal line (at the same angle) from the west coast of South America, 
under the equator, running north-eastward, strikes a headland of Greenland. 
Another line from this west coast of South America, under the tropic, strikes 
and marks the trend of the south-east coast of Spitsbergen ; another from the 
north coast of South America strikes the south cape of Spitsbergen ; another 
equally distant from the last, at a point on the coast of America, (bottom of a 
bay) , strikes the south cape of an island off Spitsbergen to the east of it (Edges 
island), this line rising from a bay on the north coast of South America, strikes 
an island of the same area as the bay.* The extreme east cape below the 
equator, on the east coast of South America, has the same bearing (exactly 30°) 
with the extreme west cape of Africa, and so on. 

A diagonal line from the cape of Good Hope, westwcird, forms the mean 
trend of the western coast of Africa; continued, this line forms the mean 
trend of the south-west coast of Greenland. Another diagonal line running 
eastward from the cape of Good Hope forms the mean trend of the coasts 
of Africa and Arabia, as the land outside would fill the area of water inside 
(including the Red Sea) . And the reader will remember that this line con- 
tinued equally divides the old world.f There is a diagonal line drawn from 
an island of the Indian ocean (50° south latitude, 70° east longitude) . This 
line, continued northward, gives the mean trend of the south-east coast of 
Asia. See also the great number of capes it lightly touches, and note the 
trend of the coast at which it enters the Arctic ocean. 

Return to the diagonal line from cape Horn, eastward, and compare it 
(as lightly touching the capes of Europe, &c.) with the preceding line (rising- 
eastward from an island of the Indian ocean) , as lightly touching the capes of 
the coast of Asia. 

The diagonals, or rhumb lines, described, will suffice to show not only 
that the general trend of the coasts is determined by law, but that the position 
of isolated capes and far off islands and even island-rocks have symmetrical 
relations. The lines open to view a oneness, — a unity of various masses of land 

*Many seas and bays have the shape and area of islands, for the cause which elevates also 

•}" The " old world" includes Europe, Africa, Asia and Australia ; and this land is divided into 
equal areas by this diagonal. The line which divides the old world, excluding Australia, is the 
meridian 70° east, which also divides the Indian ocean into equal areas. 




and areas of water all over the world. This is beautifully shown in a trend- 
line of America, which, crossing the Atlantic eastwardly, becomes the trend- 
line of coasts of the old world ; and so the trend-line of America, crossing the 
Atlantic westward, forms the trend of coasts in North America. 

There is a striking characteristic of the eight diagonal lines rising north- 
ward from the four major axes. The former pass over more water than lines 
at any other angle or from any other north and south axes. When they pass 
a coast they touch it lightly; when they penetrate a continent, where there are 
inland seas, they pass over these seas, often marking the trends of the coasts 
of inland seas. Their points of intersection generally are in the ocean, or on 
or near inland waters. 

In this feature these eight diagonals differ pointedly from the north and 
south axes of existing continents. These (north and south) axes pass over 
more land than any other meridian lines, while the diagonals from them pass 
over the greatest stretches of ocean and inland seas. It is also remarkable 
that the major axis of the Pacific, as an exception, passes over the greatest 
possible stretch of ocean, thus differing from the north and south axes of the 
present continents. 


The Symmetry, or Harmony, of the Earth's Surface-divisions, as indicated by 

Geological Phenomena. 

In an address before the British Association (1850) the received notions of 
the paroxysmal action of the earth's interior heat are given: "Even now 
geologists are measuring the rise and fall of the earth's elastic crust; and men 
who have no faith in science often learn the truth to their cost when they see 
the liquid fire rushing upon them from the volcano, or stand above the yawning 
crevice of the earthquake. Who can say there is a limit to agencies like these? 
Who could dare to assert that they may not concentrate their yet divided ener- 
gies and rend the earth to pieces." 


The force of earthquakes and volcanoes, on the other hand, is now to be 
presented as acting remedially to restore order on the earth's surface. 

The following characteristics of earthquakes are collated from Mr. Mallet's 
report to the British Association (1850) : 

Earthquakes occur all over the world, but their foci have special positions ; 
those portions of the globe which are in and around the present centres of 
volcanic action are the most subject to these convulsions; regions of extinct 
volcanoes are not specially subject to them; the foci of the most violent have 
been some degrees away from volcanoes in action ; generally they occur at a 
certain undetermined radius around volcanic centres, not far inland, but on 
sea-coasts or near them. They generally enlarge the areas of countries (Hum- 
boldt); they often occur in the ocean, far from land; their shocks or waves are 
true undulations of the solid crust of the earth; the undulation has a motion of 
translation ; they are caused, therefore, by a force acting both vertically and hori- 
zontally, which upheaves and rolls onward the coast- waves; the crest of the 
wave advances on a given line parallel to itself; lateral pressure is clearly 
indicated in earthquakes. 

A few only of the known facts of volcanoes require to be now stated. 
They are usually on the sea-coast or coasts of inland seas, (invariably so, 
with the exception of the volcanoes of central Asia ?) . The} 7 " become extinct 
generally from the west to the east.* Submarine volcanoes are frequent 
on certain lines of ocean, which are continuations of the lines of the normal 
trend of coasts. Volcanoes in action indicate an upheaving earth-crust. 

There is a large number of dynamic agents which appear under two 
phases, the one as periodical, the other as paroxysmal; the first occur under 
law, the other class as if accidentally; the latter, however, as before said, appears 
only because of ignorance. The disturbance of the needle, or "magnetic 
storms," once regarded as fitful, has been found, by the progress of science, to 
be periodical. In like manner, volcanic and earthquake action, now regarded as 
fitful and fortuitously paroxysmal, will in its turn be found to act under law.f 

There is evidently a widely- diffused, uniformly- acting force, which up- 

* Professor Dana observed that the volcanoes of the islands of the Pacific ocean become 
extinct from the west to the east. On the continents they become extinct, range after range, from 
the interior seaward. The effect of volcanic heat is usually on the ocean-side of mountains, as 
shown in the Appalachians and Rocky Mountains. 

f Traces of periodicity of earthqnake-phenomena have been shown by Mr. Mallet, in his 
record of 6,000 earthquakes. 


heaves the earth's surface, and which not only upheaves but which translates 
the upraised earth- wave from the west to the east; this wave of elevation has 
passed repeatedly, and is now passing, around the earth, burying continents 
and raising others above the level of the seas, in their places. Slow is the 
motion, and, like the growth of a tree, the change is unperceived. This, as a 
general law, but at times the earth trembles and heaves up its surface ; im- 
mense earth-waves, thousands of miles in length, parallel to themselves, roll 
along the surface of the globe, with intense rapidity ; gently, as a general law, 
but at times vast areas of land have been, and are even in our days, most sud- 
denly and violently thrust up;* without vfriction or pressure, as the general law, 
yet the volcanoes, in their fires, show the mechanical production of heat, by 
friction and pressure, created by the motion of parts of the earth's surface. 

As magnetic storms are engrafted on the periodic variations of the needle, 
so the facts of earthquake disturbances are a part of, belong to and flow from 
the regular action of the uniform force which gives the relief of continents, and 
which (of course), by its elevation of land above the level of the sea, gives the 
contour of islands and continents, and the trend of their coasts. 

The action of this force is proved to be under law, by the fact that to the 
trends of the coasts there is the often repeated angle of thirty degrees.f To 
fix and to preserve exactly this trend of coasts, nature, it may be again said, 
continually strives. Volcanic action and accompanying upheaval are found 
where this trend has not been preserved. Earthquake-action is found usually 
on the line of upheaval, in the ocean, having its focus, or axis of maximum com- 
motion, near the coast, or it is accompanied with a change of earth-level in the 
interior of continents: the insults of both actually bring the contour and relief 
of continents toward their normal conditions. 

Let the position of volcanoes be now traced (remembering that the true 
trend of coasts is at an angle of 30° with the meridian,;];) beginning the survey 

* In one instance 4,600 square miles was elevated from one to nine feet. Then in the island of 
New Zealand a range of hills and rocks was lifted vertically, while the tertiary plains were unmoved. 

fThe features of symmetry indicated by Bacon, Foster, Humboldt, Steffins, Professor Dana, 
and others, are sufficient to show a world-wide, equably-acting force. The upheaving force forms 
the contour and relief of masses of land, and the same shape is every where repeated. 

J All north and south and east and west trends of coasts (excepting in the north coasts of con- 
tinents) are abnormal. The normal trend on each side (30° angle) gives the continents their tri- 
angular shape. It will be sufficient in the examination to note the trend rising from the south as 
north-west for one side and north-east for the other side of the continents. 



at Cape Horn, South America; the trend of the south coast of Terra del Fuego 
is east and west, and there are volcanoes; thence the trend of the west or 
Pacific coast of South America, northward, from Cape Horn, for some degrees 
of latitude is nearly normal, and volcanoes are not found. They re-commence 
with the Chilian range, on a coast very abnormal, inclining to the north, — a little 
eastward. Those of Peru are on a sudden change of trend to the westward ; 
further north the coast assumes its normal trend, and volcanoes cease. The 
Quito volcanoes are found further north, on a trend to the north-east ; those of 
Guatamala and Mexico, still further north, arc on a coast which bends abruptly 
to the westward; the volcano of St. Helens is on a sudden change of trend 
to the north; and then, on a sudden inflection of the coast, near Behring's 
straits, the volcanoes are on a coast inclined to the west. 

From a peninsula of this north-west coast the Aleutian isles extend, and 
the direction of this chain is curved, and these islands are closely dotted over 
by volcanoes. The volcanoes of the coast of Kamtchatka (Asia) seem to be an 
exception to the general law of position, but these are on a ragged, broken 
coast, very distant from the east diagonal of Asia. The volcanoes of Japan are 
on an east and west trend; the Australian series, that of the Caribbean sea, 
and those before named on the Aleutian isles, have curved direction of chains ; 
Vesuvius and JEtna, of the Mediteranean, are on broken abnormal coasts. 
The Iceland volcanoes are on north and south and east and west trends. 

On the contrary, the Atlantic shores of the continents of America, Africa 
and Europe are of mean trend, at the right angle, and these coasts are without 
volcanoes ; so, likewise, the east coast of Africa is at 30° angle, and is free from 
volcanic fires from the cape of Good Hope to Arabia, where, at the Red sea, 
and on the broken trend, volcanoes are found. 

There is a small earthquake area on the west, or Atlantic coast of Africa, 
where there is a broken trend, by the westerly projection of an extended cape. 

It will be admitted, as a general law of position, that volcanoes are not 
found on coasts of mean normal trend ; and that they abound on shores with 
sudden bends, and on coasts at a distance from the diagonal lines winch mark 
the normal trends, and that these fires arc intense in proportion to the sudden 
bends and the distance of the coast from the diagonal lines. This latter law- 
is clearly seen on the west of America, and the cast coast of Asia. 

This view accounts for the fact that volcanoes become extinct generally 
from the inland of continents to their ocean shores. The inward ranges have. 
discharged their work and are at rest, and other ranges, seaward, continue to 
act where the coast is being upraised. 


The united earthquake area of commotion (Johnston's Physical Atlas), 
commencing in North America, extends in breadth (latitude) from the Canadian 
lakes to Caraccas, in South America ; this area of associated areas of commo- 
tion reaches across the Atlantic (preserving nearly one breadth) to central 
Asia. It has this striking characteristic: its boundary, in the mean, both at 
the east and west is at 30° angle with the meridian. This area connects (nearly) 
the volcanoes of Mexico and Guatamala with those of central Asia.* 

This great earthquake-area (of commotion) extends, it will be seen, from 
the centre of North America to the centre of Asia. And it passes over the one 
continent, broken by the Gulf of Mexico, and over one broken by the Medi- 
terranean. These facts show that there are special characteristics of the posi- 
tion of lands often and violently agitated. 

This question now presents itself: was it earthquake-convulsion which gave 
the broken coasts, or is earthquake-action an effort of nature to restore the 
normal relief and contour? An abnormal upheaval or subsidence may have 
thus broken the two continents, and the action of earthquake-upheaval may be 
the curative action. The perturbations of the action of the upheaving force, 
thus correcting itself, becomes a regular oscillatory movement.f Combine the 
two facts, and the reason will be found why earthquakes are on broken land, 
and volcanoes on abnormal trends of coasts. It is clear that volcanoes, so to 
speak, mend the trends of coasts ; has not earthquake-action, on broken land, 
the same office? In answering this question consider what may be called the 
sameness of the action of the force of the world. Europe and Africa were 
raised up by a law, and the basin of the Mediterranean is left under water. 
The same law which elevated the coasts of this sea is yet in action, to elevate 
its water-bed ; and islands are thrust up there, some of which remain fixed in 
their elevation and some disappear. 

Earthquakes level mountains and upraise others ; they fissure the earth's 
surface; they form new valleys and erase the old; they bury cities, appearing 
as frightful catastrophes. But, all past volcanic action and all the throes of 
earthquake have resulted, on the whole, in a symmetrical configuration of the 
earth's surface, therefore, earthquakes so far from marring, have contributed 

* There is an isolated earthquake area, that of the Red sea, equal to an isolated area off Chili, 
South America. 

fit should be remembered that earthquakes enlarge the area of continents, — for an instance : 
one earthquake of South America raised the west coast some four feet, and over more than a 
thousand miles, and this in one night; volcanoes also mark upheaving-coasts. 


to create the symmetry, restoring to the right condition the relief and outlines 
of the earth's surface -divisions. 

Bold as this hypothesis may appear at first, it is true to nature. In meteo- 
rology it is ascertained that the temperature of any two opposite hours of the 
day gives, in their mean, the mean temperature of the whole day. Yet devas- 
tating storms suddenly take place, and the peace of nature often appears to be 
greatly ruffled in parts of a day. 

Is it not true then that the sudden storm and long continued calm, abrupt 
changes and long continuation of one degree of temperature, are equally the 
parts of a perfect system? Is not a sudden tornado which changes the tempe- 
rature of some hour of the day, one fact of a system, as the change enters as 
an element of the mean? Yet the storm puts on the appearance of an acci- 
dental paroxysm of nature; it overthrows trees and buildings, it blasts the 
hopes of the agriculturist, and it strews the coast with wrecks. So the earth- 
quake wears the fierce face of paroxysmal action, rending and destroying. It 
is also, however, a normal fact of a harmonious system of facts which, com- 
bined, give the normal contour and relief of the continents. 

To repeat: A symmetrical earth with earthquake-convulsions can only 
exist under the condition that these convulsions are agents in determining the 
harmonious relation of its surface divisions. The diagonal lines at 30° angle 
with the meridian being the true trend of the coasts, (and mainly the actual 
mean trend or boundary of the relief of the continents,) are lines of flexure .* 
They are the dividing lines of upheaval and subsidence. They will, therefore, 
be found deeply characterised by earthquake-phenomea ; and, at the intersec- 
tion of these lines of coast-trend the phenomena will be intensified. \Yith this 
hypothesis let the map be re-examined. 

The western diagonal of America. This line passes from Terra del Fuego 
(itself containing volcanoes) , northward ; as it passes over the Pacific ocean its 
track is marked by submarine earthquakes, volcanoes, floating pumice, and 
other marks of this agency .f Off Chili it forms the western boundary of the 
Chilian earthquake area; and here islands have been thrust up (which often 
sank) during a violent volcanic-action on the coast. It intersects, at Behring's 
straits, with the east diagonal of Asia. Now, here also converge to a point the 

*"It may, and probably will, yet be established that there is an intimate connection between 
the cause of volcanic phenomena and the upheaval of the north-west and south-east and north- 
east and south-west ranges" (or trends). — Mr. Butler's "Philosophy of the Weather" page 217. 

fThe facts of position are all from Johnston's Physical Atlas. 



volcanic range of eastern Asia and the volcanic range of western America. 
Here meet also the chain of the old Rocky Mountains of western America, 
with the mountain-chains of eastern Asia.* 

The east diagonal of America passes from the volcanoes of Terra del Fuego 
to the middle of the Atlantic, and there, near the equator, it intersects with 
the west diagonal of Europe- Africa : here, at this intersection, are submarine- 
volcanoes, and here the basin of the ocean is upheaving. Then the east diag- 
onal of America, after the intersection, passes near Lisbon, the noted centre of 
the most extensive earthquakes which have shaken the solid foundations of the 
globe. This line then touches England, and England is often slightly earth- 
quake-rocked, especially in the range of this line.f Afterward, this diagonal 
traverses Scandanavia, where there is a modern upheaval of earth-surface, 
which is still in progress ; and here it intersects with the west diagonal of Asia. 
Norway is earthquake-ground. 

The west diagonal of Europe-Africa passes over the submarine volcanic 
area of the mid -Atlantic; J on the northern Atlantic it runs over an area of 
known uprising of the bottom of the sea. In this track large islands have 
been suddenly thrust up, which soon after again sank ; the line, after this, 
is over a coast of known modern changes of surface. 

The east diagonal of Europe-Africa passes up the Indian ocean, over 
archipelagoes of small islands, shallows, and sand-banks, and it enters Asia at 
the centre of the Cutch earthquake area;§ and here also have large areas of 

*M. De Beaumont regards this meeting place as the commencement of a rent or fissure of 
the earth's crust which, widening to the south, formed the basin of the Pacific ocean. It is not, 
however, an accidental separation. The point of separation bears at the angle of 30° with both 
the south terminations of the major axes of Asia and America. 

fThe line enters England near the Lands-End, and passes over the coasts of Cornwall and 
Devon. This coast is distinguished for earthquake-action and abnormal tides or ocean-waves, — 
the water running rapidly in and out of the harbous, in oscillatory motion. The bay of Penzance 
is noted for an intensity of this earthquake-phenomenon, for it is admitted that these waves are 
from motion of the bottom of the sea. These waves are similar to those which occured on the 
shores of England, before and during the great Lisbon earthquake. 

J Midway of the Atlantic, on or near the equator, soundings have been obtained at 400 fath- 
oms. Here earthquake-shocks are continually felt by passing vessels. — Mallet. 

§ South of Hindostan there is a known change of level of the basin of the sea. Both the 
great Cutch earthquake and a disastrous earthquake in Persia had their course south-west to north- 
east, on this line. 



land been suddenly thrown up, some of which afterwards sank.* The diagonal 
enters Asia, and on this line in central Asia, and where the Australian west 
diagonal intersects it, are the interior volcanoes of this continent, 1,500 miles 
from any ocean. f 

The west diagonal of Asia intersects the east diagonal of Europe-Africa 
near to the Cutch earthquake area,| The west diagonal of Asia also intersects 
the east diagonal of America, in the vicinity of the Baltic sea (upraising level) , 
and it passes to Greenland, where, under both intersections, are changes of 
land-level in progress at this era. It intersects here with the east Pacific 

The east diagonal of Asia skirts a long range of volcanoes and passes to 
Behring's straits. Near this intersection is a range of intensely active volca- 

Follow the west diagonal of Australia north: it passes, before entering 
Asia, over the fierce volcanic area of the Indian Archipelago; at its intersec- 
tion in central Asia, with the east diagonal of Europe-Africa, are the interior 
volcanoes of Asia. 

There is an earthquake area in the valley of the Mississippi, of which 
New Madrid is the centre. This centre is on the east diagonal of the Pacific, 
and at the intersection of the diagonal equally dividing this continent. The 
western diagonal of Australia passes over the volcanoes of central Asia. The 
east diagonal of the Pacific strikes the uprising coast of Greenland. 

The line or axis of synchronous action of the North American earthquake, 
as traced out by Professor Rogers, is inclined 30° to the meridian ; and the 
axis moves eastward, parallel to the eastern coast. This is also the major 
axis of the winter storms, as traced out by Mr. Espy. The chain of the Apa- 
lachians is 30° inclined; and also the chain of the Rocky Mountains is 30° 
inclined. In very many earthquakes, trees, spires, &c, at first bow or incline 

*By the earthquake of Cutch (in 1819) the bed of the eastern branch of the Indus, previously- 
one foot deep, suddenly obtained a depth of twenty feet. — Mallet. 

■(■"The great distance from the sea," says Humboldt, "of the volcanoes of central Asia, is a 
remarkable and solitary phenomenon." 

| The west diagonal of Asia extends across Persia (earthquake ground), to the Caspian sea: 
"An earthquake region extends over Asia Minor, Syria, and Palestine, to the Caspian sea, and the 
Caucasian Mountains." "Persia and the Caspian sea form the link between the Mediterranean 
volcanic district and the district of central Asia, in one direction, and the south Asiatic district in 
another direction." 



to the south-east and then to the south-west, in oscillatory movement. The 
cleavage plane of the rocks of the valley of the Mississippi * as measured by 
Professor Brainerd, and as a general law all over the world, is, in the mean, at 
30° angle with the meridian. f 

There are some general facts which bear on this branch of the subject 
(which Pliny calls the "crimes of nature"), apparently with great force: the 
persistency of the location of earthquake-areas, the north-east and south-west, or 
north-west and south-east direction of the shocks (concussions) ascertained by 
the oscillation of trees, &c; the general ocean-origin; that earthquakes are 
generally preceded by ocean-waves on the coast ; and the reader will remember 
that the position of the diagonals is generally over oceans, and near the coasts. 
lso the synchronous existance of earthquakes on the same lines bearing at 
30° angle with the meridians. 

Coincidence of storm and areas of earthquakes and broken lands : The rise 
of the West Indian hurricanes; the Typhoons of the Indian ocean; the storms 
of the bay of Bengal; the Cyclones of the Mauritius, are over islands and 
broken land, which are also the volcanic or earthquake-areas. The storm- 
region of Cape Horn is off broken coasts and islands. The great Atlantic 
storm of 1836 was from the broken lands of Nova Scotia to the ragged south 
coast of the Baltic. Storms rage in the English Channel, and on the ragged 
coast of northern Europe. Our great lakes are storm-regions. Storm tracks 
often unite distant volcanic districts, for instance, the Cape de Verde and 
the Canary isles. The storms of the Pacific are usually over its archipelagoes ; 
and this ocean has its general calmness, because of its vast area of water unbro- 
ken by lancl.J 

Attention is now directed to certain dotted lines of the map, which form 

*The cleavage plane of rocks, it is now generally believed, is from lateral pressure. " The 
coincidences," says Professor Dana, » confirm the view that the ranges of mountains and islands 
correspond to the range of fissures." Lateral pressure is clearly indicated by the compressure 
(distention) of rock-enclosed fossils. 

-j-The major axis of the area of commotion of the great Lisbon earthquake, (as shown in 
Johnson's Physical Atlas) is inclined 30° to the east diagonal of America. This area of commo- 
tion was bounded north in Europe, and west in America by the intersection of diagonal lines. 

X Let one instance be specially noted : the Aleutian islands are highly volcanic ; then turning 
to the English Encyclopedia (Geography) it is found : " It can be hardly said these islands have 
any summer, for fogs and rains are of daily occurrence; the weather is very unpleasant in winter, 
on account of the sharp north-east and north-west winds. 


the sides of equilateral triangles.* Each side is 42° arc, being cognate dis- 
tances, or measures, which are of equal length on a Mercator-map, while on a 
sphere the distances lesson as the degrees of longitude diminish. The lines 
are either east and west or at an angle of 30° with the meridian. They subdi- 
vide the continents, being unities, or integral parts, of the great unities of sur- 
face division. The character and use of a few only of them will be given, as 
the explanation of these will lead to the comprehension of all which are drawn 
on this, and which may be drawn on other maps. 

To commence with those on the east coast of the United States, running 
northward : these three lines measure the stretch of land under them ; where 
the coast at the north is projected the coast at the south also rises north, so 
that, under the three lines, from ocean to ocean, there is the same extent of land; 
the figure of the coast south matches and is correlated with the coast at the 
north termini of these lines. This symmetry alone might be regarded as an 
"accident," but the result is, because of a general law. On the west coast ot 
North America is a projection of the coast, by an archipelago, the islands of 
which form almost a peninsula. Two of these lines, of 42° arc, and at the same 
angle, one on each side of this break of coast-trend, reach north to ocean, one 
to each side of an indentation of the northern coast. Again, two of these lines, 
are each from the break of the coast-trend of the peninsula of California, to the 
south coast of ITudson's bay. This clearly indicates the oneness of the system 
of the earth's geographical divisions ; because the marked features of the coast 
line have the same bearing over land as across the oceans; and these marked 
features of coasts are at one (cognate) distance from each other; and this nor- 
mal distance applies over water, land to land. For instance : the arc 42° is 
the breadth of Australia, over land ; it is also exactly the breadth of the Medi- 
terranean sea, over water ; and the line reaches from the extreme north coast 
of Nova Zeinbla to the coast of Europe, over ocean. 

Where these sides of the triangle do not measure from coast to coast they 
reach to inland seas. For instances of this : the two lines from ocean, running- 
south, reach to the great lakes of North America, as has been shown ; from 
ocean south to the Caspian, Black and Mediterranean seas of Europe- Asia.f 
In fact the ocean coast seems to throw out its capes and draw its line back into 
bays in order that the normal stretch of land may be obtained. 

* In some cases only one side is given to avoid complexity ; the eye can complete the triangles. 
fThe Aral sea, of Asia, and two northern lakes, of North America, are thus located. 


And again, when this described termination is not attained, and when 
these lines from the sea coasts do not measure the land or terminate at inland 
seas, there is volcanic or earthquake action at their inland termination. For 
instances of this : lines from the broken coasts of Hudson's bay terminate in 
the valley of the Mississippi, at or near New Madrid, which is the focus 
of earthquake disturbance. So, lines from the coast of the oceans around Asia 
terminate at the volcanic district of central Asia. Lines from the opposite 
coasts do not measure the distance of Iceland, but overlap into the interior of 
this highly volcanic island. Many of these lines fall short of reaching land, 
terminating in ocean, near the city of Lisbon, also near Caraccas, (South 
America), and in the Caribbean sea. 

These lines have a special relation to the north and south axes of conti- 
nents. Thus, as before shown, on the tropic, 42° arc extends from the north 
and south axis of Europe- Africa, east and west, to ocean. These lines also 
reach from the north and south axis of America, eastward and westward, to 
ocean, (say in latitude 68° north) ; and from the axis of Asia, westward and 
eastward, to ocean, in say latitude 75° north, 

The coasts, as before said, protrude their capes and headlands to produce 
this symmetrical extent of lands, the lines reaching from ocean to ocean. Let 
one instance of this result be specially noted : 42° arc extends westward from 
the American axis to water into the arm of a bay (below the parallel of say 
68° north); this arm, or extension of the bay, is not therefore from a "parox- 
ysm." Dotted lines extending from this bay (as before shown) point, south- 
westward, to a broken west coast of America; and also, south-eastward, to the 
great inland seas of North America. From the broken coast of western 
America to the Sandwich isles, the distance is measured by a dotted line; 
which line terminates on another dotted line of 42°, which reaches, east, to the 
southern point of the Californian peninsula; thence a dotted line reaches to 
the north and south axis of America; thence north, on this axis, to the point 
on which the examination began. 

The termini of these lines which spring from the diagonal lines, marking 
the trend of the continents, are on strongly marked earth-points. For instan- 
ces : a dotted line runs from a diagonal through the valley of the Mississippi, 
an axis of modern upheaval, and it falls short of reaching Caraccas (South 
America), which is an earthquake -focus. In South America one of these lines, 
from the east diagonal of America (at the mouth of La Plata) , falls short of 
reaching the western volcanic coast of this continent; another of these lines 
from this diagonal, under the tropic, overruns the land, and terminates in a 


volcanic area of the Caribbean sea. These lines, from the diagonal, crossing 
North America, at the great lakes, terminate at an indentation of coast, These 
instances will suffice. 

It is possible, by the aid of this triangulation, to lay out unknown coasts, — 
the triangulating lines teaching of unseen lands. For instance : the continuation 
of these triangulating lines on each side of the strait which leads to the open 
Polar sea, forms the mean trend of the coasts recently discovered.* The 
world's surface should, therefore, be studied by completing the triangulation 
on a map of large scale, with accurate outlines; for, the accompanying map 
is sufficient only to set forth the principle of these subdivisions of the earth's 

Three of the triangular divisions of land will be examined : The first, on 
Australia, has its base on the southern coast ;f its apex or north angle reaches 
exactly to a northern coast of New Guinea, which is connected to the main 
land by a submarine relief. This distinct subdivision is altogether without 
volcanoes. Another triangle is drawn on the south of Africa, its area is all 
land, except at its north-west angle ; and the ocean where the triangle overlaps 
is greatly volcanic ; and north, in Africa, there is a small earthquake area. 
The triangle on South America has its base where 42° measures its breadth on 
the tropic; its apex is on the west coast; and where its north-west angle over- 
laps into ocean there are submarine volcanoes; and where its westward side 
enters the land there are coast- volcanoes.J 

* One of these lines, showing the trend of these northern coasts, rises from a marked point 
of the Pacific ocean. 

^Australia has a southern coast which runs east and west, and thus differs from the south 
coast of all other masses of land. 

J After drawing the diagonals the author read an article in the Edinburgh New Philosophical 
Journal (vol. 55, p. 165), and found that Mr. Hauslab, from his geological investigations, came to 
the opinion that the surface of the globe presents, approximately, the face of a great octahedron. 
One of the circles which point out the limits of the faces of the crystal is coincident, nearly, 
with the east diagonal of America, and one embraces the arc 138°, described in page 9 of this 
Treatise, from the west coast of South America to the east cape of Arabia, under the tropics. M. 
Boue accepts these views of M. Hauslab, and adds that the metals crystalise in the tesseral or 
rhombohedral systems, and that native iron is octahedral in its crystals. 




A Discussion of Meteorological Phenomena. 

In an annual report of the Greenwich observatory, the Astronomer Royal 
speaks of the results of his meteorological observations as useless for the want 
of even empiric theory to bind them together into a system, thus distinguish- 
ing them from the results of astronomical observations for which he has a 
system. The views of some distinguished meteorologists are held as provis- 
ional; they are not fully satisfied with the current hypotheses. The backward- 
ness of this branch of science is usually attributed to the complexity of the 
causes which act to produce the vicissitudes of the weather. But the complexity 
of assigned causes is not the reason, but is the sign of backwardness. All 
branches of science, in their infancy, are characterised by an intricate maze of 
assigned causes, and by a complexity of hypothesis. This was the condition 
even of astronomy before Copernicus, Kepler and Newton gave to this science 
unity and simplicity. 

The fundamental error in meteorology appears to be that it assigns as the 
cause of each, the action of other weather-vicissitudes. The science reasons in 
a circle, ending where it began. Thus, it declares that the winds blow because 
of a want of equilibrium in the atmosphere ; the unbalanced atmosphere is 
attributed to variations of temperature; change of the temperature, it is said, 
produces evaporation and precipitation ; precipitation and evaporation produce 
changes of temperature ; and these latter produce the blowing of the wind, 
which completes the circuit; and the meteorologist is where he began his search. 
No solid ground has been attained on which to base the vicissitudes of the 
weather beyond these vicissitudes themselves. The atmosphere has been cut 
off and separated from the common pulse of motion of the whole earth. Its 
air-currents are because of themselves, as if the atmosphere were not a con- 
nected part of the world, and had no relation whatever with other dynamic 
phenomena. And this, when it must be an admitted fact that meteorological 
phenomena are closely connected with physical geography and geological phe- 


The following question was asked by a learned meteorologist: "Who can 
tell how the soft and balmy air, which hardly resists the motion of a lady's 
fan, can exert a power sufficient to level to the ground the largest trees of a 
forest in a single minute?" Let it not be understood by these remarks that 
nothing of importance has been accomplished in this branch of learning. The 
oceans are more safely and swiftly navigated because of the labors of Mr. 
Maury. Predictions of the coming weather are often rightly made by reason 
of the investigations of Mr. Espy. Prof. Henry has collected many facts of 
the weather- vicissitudes of North America, the knowledge of which is import- 
ant to the agriculturist; and which have been broadly disseminated in the 
Agricultural Reports of the Patent Office. Nevertheless, there is no philoso- 
phy in the science, for fundamental questions are not answered by existing 
hypotheses; and this is acknowledged in almost every treatise on the subject. 

It is believed, by the author, that this science requires some common 
ground for all weather-vicissitudes ; and thus to be brought into correlation 
with other sciences. The limbs of a tree do not bend because of each other's 
motion, but all wave because of a common cause, — the blowing of the wind. 
The strength of a man's right arm is not derived from that of the left, when 
both are used for a common purpose or result. "La verite est tonjmtrs sem- 
blable a elle meme de quelque cote qyton la regarded Volcanic action and earth- 
quake movement have certain relations to each other, in time, position and 
results, but one is not the cause of the other. They are two phases of a 
remedial dynamic act of nature; and the winds, clouds, rain, and so on, are 
also phases of *>ne action, which phases, singly or combined, restore the normal 
condition of things, as will be after explained.* For instance: A ship sailed 
some degrees of latitude beyond and within the usual limits of the trade-winds 
without experiencing them, — the wind blowing in an opposite direction. Sud- 
denly, one evening, there arose a violent storm, "it was awful," said the narra- 
tor, "the flashes of lightning had no perceptible interval of division, and the 
roar of the thunder was continuous." The storm subsided into a perfect calm, 
and soon after the trade-winds set in with such intensity that the ship for days, 
under reefed topsails, was swiftly borne on her course. This fact, however, is 
hardly needed, as every one has felt that condition of the atmosphere, after a 
storm, in which the mere act of breathing is enjoyment, and knows that storms 

* The storm areas and volcanic and earthquake areas have been shown to be coincident. 


have another function than that of restoring the equilibrium of the atmosphere.* 
Both earthquake-action and weather-vicissitudes are not only remedial, but 
often they act together. The following earthquake-facts are from Mr. Mallet's 

'"A feeble streak of light in the heavens (northeast to southwest) in the 
direction of the shock for twelve or thirteen miles, and balls of fire seemed to 
come from it.' -Accompanied with a loud noise, a brilliant light in the heav- 
ens and an auroral arch.' 'A strange star of an octagonal shape, which 
seemed to throw forth balls of fire.' 'Each shock was preceded by a rushing 
noise like a gust of wind.' 'The sky was obscured, in which red rays were 
observed converging near the zenith.' 'A black cloud, with continued and 
confused flashes of lightning, had been visible, the latter ceasing just before 
the earthquake.' 'Preceded by a dreadful noise and followed by a violent 
storm.' 'A clap of thunder with a clear atmosphere.' ' Paleness of the sun 
as usual.' 'Vapors of strange character, heat excessive.' 'A strange light 
appeared.' 'Stones were thrown from the walls.' 'Followed by diastrous 
rains.' 'A luminous cloud driven with violence.' 'From time to time the 
wind would become stronger and then cease, and at the moment of its ceasing 
the shocks would recur.' ' Preceded by an extraordinary calm, the stars spark- 
ling brilliantly.' 'The atmosphere appeared as if on fire.'" 

Humboldt speaks of the "mysterious connexion" between volcanic phe- 
nomena and rains. The bursting forth of a volcano in South America, he says, 
will sometimes change dry into rainy seasons. So in Europe, on the 19th of 
December, 1821, a violent eruption commenced from a volcano of Iceland, 
which had been quiet since the year 1612. On the very day of the commence- 
ment of this eruption the waters of the adjacent rivers were greatly swollen, 
and all over Europe dreadful storms of wind, hail and rain succeeded. 

Thus it is seen that often the two classes act together ; not that one pro- 
duces or causes the other; both exist as remedial agents. 

Descartes thought that one, and only one degree of force was in action on 
the world ; and that the force acting upon any moving body was communicated 
on the stoppage of the motion, and gave motion to other matter. But this 
great truth was not generally received, on the ground that bodies often cease 

* On the west coast of Africa tornadoes occur on the change of the wet to the dry seasons. 
The equinoxes mark a planetary change of the earth, and there are usually equinoctial storms. 


to move without any evidence of a transfer of force. There is, however, an 
intense invisible motion, which God hides under the veil of uniformity, — the 
force by which the earth revolves and rotates. This is unseen and unfelt, as 
all things move equably and together. It is divergent or relative motion only 
which manifests itself.* 

Now, on the face of things, it appears in a sudden and violent storm as 
if a new force had been induced and brought into action. It cannot be so. 
There is no more force in action, on the whole, when the storm-wind is rending 
the limbs and even bending the trunks of the stubborn oaks, than when a 
gentle breeze wafts on slowly and smoothly the buoyant down of a thistle- 
seed. The storm's force is a spray lifted into sight from a hidden ocean of 
energy. The action of this spray of force gives visible, because it gives 
divergent or relative motion. When the storm ceases, divergent motion no 
longer exists, as the force has returned to give equable unseen planetary 

This answers the question: the placid, balmy air, which hardly resists the 
motion of a lady's fan, drinks of the waters of the unseen ocean of force, and 
becomes at once so strong as to overthrow a forest of trees. 

The air is an agent of transfer; it absorbs force in one earth-position, 
moves as wind, and on the cessation of its motion it has delivered up its force 
at another earth-position. 

The hypothesis presented is that all weather-vicissitudes are dynamic 
agents, the function of which is to restore, not the equilibrium of the atmos- 
phere only, but to maintain the right condition and equable action of the 
empyreal force or energy which constitutes the life of the world. 

Heat: It was the opinion of Newton, — and the truth of this view has been 
recently proved by experiments, — that "heat consists in a minute vibratory 
motion of the particles (atoms) of bodies." Heat is work, — living force ex- 
action.-)- All mechanical means for its production resolve themselves into one 
condition : force (vis motrix) is applied, and the progressive motion of the body 
to which it is applied is restrained or impeded. In other words, heat is 

*A stone lying on the earth's surface has intense motion in its daily axial rotation; but it is 
invisible motion, because all things near to and about it move with it. If the stone Calls it is 
relative or divergent, and consequently visible motion. The stone in falling is also rotating in a 
divergent orbit of rotation. 

f This hypothesis was originated by Lord Bacon. (Nov. Org.) It was taught also by 



induced by friction impeding, and by pressure preventing, motion.* If a piston 
is driven down into a closed tube the force applied is not lost; it gives motion 
to the atoms of the contained air. The heat of a steam-furnace impels 
machinery; but if a wheel of the machine, by friction (or impeded motion), 
has its velocity retarded, so that it is not of the degree due to the force applied, 
then atomic motion, which is heat, ensues. Thus, the rubbing together of iron 
plates will warm a large apartment for many years.f 

Let a fundamental fact be here recognized: God's force is never defrauded 
of its work.J It must act of necessity. Water in freezing delivers up force, 
(vis motrix) and if contained in the walls of a solid rock the rock will burst, as 
its parts must have motion from the evolved force. Let cold iron be struck 
on an anvil, it will become heated: that is molecular motion will be induced: 
the force from the workman's arm is not lost; it cannot give progressive motion 
to the mass of iron as a whole, it therefore induces molecular motion; that is, 
by the applied force, the iron becomes heated. 

To repeat the expression, force must necessarily produce motion. In 
opposite currents of water the friction stops the progressive motion of a part 
of the Avater, and this arrested water continues the motion in whirlpools ; a 
piece of paper in falling often rotates, for its descent is impeded by the air, 
and it has not the velocity of descent due to the distance it descends, it therefore 
rotates. An arrested floating iceberg rotates. § 

*A certain degree of molecular motion belongs to each body, according to its kind or chemi- 
cal character. This is a degree of heat or molecular motion which each can retain, and which is 
the normal or abiding atomic-motion. It is their latent heat. If the molecular-action is urged 
beyond this the heat is radiated, — that is, it gives molecular-motion to adjacent bodies. If force 
is so suddenly applied tiiat it cannot be radiated the solid body becomes fluid, and the fluid a?ri- 

■j- Thus in nature the friction (arrestation of part of the motion) of the wind passing over 
water warms it ; and the friction of the Gulf Stream and its gradually reduced velocity are sources 
of the heat of the waters. Can it be supposed that the friction of this great ocean-river on its 
solid banks will not give out heat, when the friction of water through a sluice-gate raises the tem- 

\ Some philosophers consider force as motion itself; that is, that nothing exists but motion. 
This is a metaphysical refinement, — practically, the cause of motion or force is ever admitted to 
exist. There is a God and a material creation, a man's mind and his body, so there is force and 
consequent motion. 

§ The descent of a body to a lower level of rotation gives force for motion in proportion to the 
degree of descent. 


The conditions of the production of heat are: the restraint of the impelled 
body, and a position or condition of this body, in which the force cannot be 
radiated, nor move larger parts of the mass than the atoms of which it is 
composed. On this doctrine the fact of the heat of volcanoes (atomic-motion) 
and the facts of the wild motions of parts of the earth in earthquakes, receive 
their solution.* And also on this doctrine will be founded the true theory of 
meteorological vicissitudes. 

Let it be re-repeated that "Nature is simple in her actions and is always 
conformable to herself."f Thus the formation of vapour and the precipitation 
of vapour into rain or cloud, hail or snow, supplies force, acting either as heat 
(molecular motion) or as giving progressive motion. 

The fundamental principles presented are, the conservation of force (its 
indestructibility), and that heat is a phase of the action of force. Force, mat- 
ter and space are in due degree relativly to each other. There are, however, 
oscillations, or temporary swervings from an equilibrium. Then meteorologic 
vicissitudes transfer force from where it superabounds to another field of 
action where it is required. 

All the philosophers of the age incline, if they do not fully assent, to 
the doctrine of a unity of force which exhibits itself under the phases of 
electricity, magnetism, heat and motion. JN T or was the idea born into the world 
in these latter days ; according to the Pythagoreans and Platonists there is a 
life infused by God into all things, — "an inward principle, producing and 
forming within, as art does without; regulating, moderating and reconciling 
the various motions of the parts of this mundane sphere.";}; 

If parallel conducting wires are placed some hundred feet apart, and a 
current of electricity is sent through one, an induced current will flow back 

* It is a very significant fact that water contained in vessels often rotates during earthquakes. 
Earthquakes are because of a partial arrestation or retardation of the planetary motion of parts 
of the earth : unused force gives rotary motion. The heat of volcanoes is from pressure or 
retarded upheaval, by the planetary force in action upon portions of the earth. Whence conies 
the force which melts and ejects the lava, but from arrested planetary motion? 

f Newton. 

J The discovery of Faraday: that oxygen, a constituent part of the atmosphere, as its tem- 
perature rises, diminishes its paramagnetic force; the phase of force resolving itself into the other, 
and the reverse. 


through the other. This is known from an experiment by Professor Henry; but 
experiments are not now needed, as telegraph wires declare the truth. The 
lightning, aurora and earthquake, each sends currents through the telegraph 
wires. A violent wind at one part induces currents of electricity. Precipita- 
tion, also, at one point, induces currents along the wire. This teaches the hid- 
den things of meteorology : the vicissitudes of the weather restore the equilib- 
rium, not of the atmosphere only, but of force, as the life of the Avorld. 
Weather- vicissitudes complete the circuit; they establish the equilibrium. 

Matter influences the motion of other matter only by the transmission of 
energy. It is force which 

" Sweeps through the dull, dense world, compelling there 
All new successions to the forms they wear." 

It is by the diffusion of force, giving the position of every atom, that the order 
of the universe is preserved. This oneness of energy, which constitutes the 
life of the world, is heard in the rustling of the forest leaves, and in the roar 
of the fierce storm. It is seen in the auroral arch, in the volcano's blaze, and in 
the lightning's flash. It is traced out in the forming clouds and the descending- 
rain. It shows itself, in miniature, in the oscillations of the barometer, and 
in the trembling pulsations of the magnetic needle. Its full majesty is mani- 
fested in the swift motion of the majestic spheres around the central luminary, 
— the sun. 

The transfers of force act, not in the atmosphere only, but within the solid 
earth. Conducting wires from two metalliferous lodes have been used to elec- 
trotype. Wires with earth-connections at their termini show the passage of 
force up the mountain for twelve, and from its summit down to the base also in 
twelve hours, in semi-daily oscillation; and conducting wires, on a level, show 
this oscillation, with termini having east and west earth-connections. 

Before the sea-breeze sets in, the mountains of islands are cloud-capped. 
Force is needed, and there is precipitation. More force is required, and the 
wind from the ocean supplies it. To repeat: nothing commences to move with- 
out receiving force, and nothing stops in progressive motion without imparting 
force. Force docs not lose itself, and the earth-point to which the wind blows 
receives the force. And in addition, underground currents of force are rising 
from the valley to the summit; and thus land and sea, and valley and moun- 
tain breezes are proportional to the altitude of the coast above the level of the 
ocean, or that of the mountain above the mean coast of the earth's surface. 
Why is this continual transmission of force required? The planetary velocity 



of parts of the earth varies hourly, daily, annually and secularly.* It is seen 
at once that this must needs be. For one instance: an earth-point now under 
the sun's meridian will have its orbit of revolution, at midnight, enlarged some 
twenty-five thousand miles. At the equinoxes the earth's axis is perpendicular 
to the ecliptic, and at the solstices this axis is out of this perpendicularity.'!' 
At the equinoxes there are storms; and the trade-winds and gulf-stream 
alternate further north and south at the solstices. There is, as it were, a con- 
stant act or effort of nature to re-adjust her forces relatively to the planetary 
position of parts of the earth. This is an ultimate fact for which a reason can 
only be given when a reason can be given for the motion of the earth itself in 
its orbit. "Deus Vult" is a point at which proud philosophy must ever bow, 
however far it may safely carry its investigations.! 

Man requires mechanical force, — that is, living or working force. He 
makes the motion of one supply force for the motion of another body. The 
rising of the wind absorbs force, and on its subsiding it yields up its force. 
Man also obtains working force from evaporating water (changing it into steam); 
the developed force thus works for him. Nature's operations are thus imitated : 
for evaporation and condensation receive and supply, — re-distributing the 
energy of the world. Man borrows the force of nature to do his work. As a 
beautiful instance of this: water, falling by a planetary force, is arrested in its 
descent, and the force of gravity is thus turned aside, and is the impelling force 
for mechanical processes. § 

# A sphere could not rotate while revolving without a constant new distribution of force, nor 
could its continents be raised or depressed, nor the level of its oceans change, without this new 
distribution. The rain all over Europe, when an old volcano came into action, was for a supply 
of force for an elevation of the continent. 

| Alternately, each pole of the earth has the larger and less orbit of revolution. 

J The received philosophy teaches that the earth moves by a hypothetical (former) projec- 
tion; that, once moved, there is nothing to stop the motion. The laws of motion analysed are 
only statements of the facts of motion, though at first-sight they appear to five lio-Iu on the 

§ At one time it was raining from the Gulf of Mexico to north of the great Canadian lakes, 
and from the base of the Rocky Mountains east beyond the Atlantic shore of this continent. It 
is well known that evaporation absorbs force, and evidently this vast area of precipitation sup- 
plied a needed addition of planetary force. Thus rain falls not merely to water the earth; and 



There is a truth which ere long will be established in all philosophic 
minds: the normal relation of force to matter is equality of distribution; and 
combining its action in its two phases, — that of giving molecular motion (or heat) , 
and that of giving progressive motion to masses of matter, — this equality is 
preserved so far that there is no abiding variation, — the want of equilibrium 
being as a transient condition. For an illustration: the orbit of the daily 
rotation of the summit is greater than that of the base of a mountain. Never- 
theless, there is an equality in the distribution of force through all the parts 
of the mountain: on the summit a larger proportion of force is in action for 
the greater velocity of axial rotation, and there is less for atomic motion, or 
heat. On ascending, therefore, the heat is found to decrease with great regu- 
larity. As cold (absence of heat) increases on the ascent from the mean level 
of the earth, so the heat increases as the earth's crust is penetrated. Is it 
philosophical to impute the cold of a level higher, and the heat of a level 
lower, than the earth's mean surface, to different causes? 

God warms the earth by a surplusage of planetary force.* The degree of 
force ever in action is nicely adjusted, or determined in value; and force always 
exists of one degree in the sum of both of its phases of action. Changes of 
temperature are, therefore, oscillations around a fixed mean, the oscillations 
being a reception from and a bestowal to planetary motion. 

This doctrine seems to be proved by the following facts : Changes of plane- 
tary velocity of parts of the earth are uniform, — periodically returning; there- 
fore, the secular mean -temperature of the earth is ever preserved; therefore, 
also, there is one stratum of the earth, under its surface, that has its tempera- 

it is beautiful to perceive that even the equilibrium of the planetary force of different parts of the 
earth is preserved by an act which waters the earth and renders it habitable. After a damp easterly 
storm a drying wind sets in. A cloudless sky has positive atmospheric electricity; a drying wind 
imparts, a damp wind absorbs force. A drying wind is from west to east, in the direction of the 
earth's motion ; a damp wind usually is the lading behind of the air, it has less force and does 
not keep up with axial rotation of the earth's surface. 

* These questions are presented for consideration : Does rot the sun give out heat to the plan- 
ets because this central luminary has not, — as the planets have, — a motion of orbital revolution, 
and has, therefore, a surplusage of force to distribute for heat, or atomic motion? Is not winter's 
cold because of the increased orbital velocity, from the enlarged orbit, first of the north and then 
of the south pole, by the changed angle of the earth's axis with the ecliptic ! Is there not an open 
polar sea, because diurnal rotation is there almost nil, and there is greater force for aton,ic motion ? 


ture never disturbed;* therefore, there is one stratum of ocean water, all over 
the globe, of one temperature; therefore, the trade-winds blow with perfect 
uniformity year after year; therefore, also, are all the periodical weather- 
vicissitudes, -j- 

There is required in the science of meteorology a oneness of idea that 
shall correspond to the oneness of the acts of nature. It is seen that 
storms arise over broken lands; and over broken lands the volcanoes blaze, 
and earthquakes shake the surface of the earth .J Near volcanoes the surface 
of the ocean water boils up as if in a cauldron. The wind often howls fearfully 
over the volcano in action. The earthquake changes dry into rainy seasons. 
Magnetic currents pass over the wires when the wind blows and when pre- 
cipitation ensues at one end of the wire. The auroras and lightning throw 
forward through the wires induced currents. Auroras and lightning disturb 
the magnetic needle. The earth's lines of equal temperature (isothermal s) 
remarkably coincide with the magnetic lines of equal dip and intensity. § 
"Heat and electricity act strangely on magnetic force." There are daily, 
monthly, yearly and secular variations of the needle, and of the intensity of 
magnetic force; these changes are connected with the periodic weather phases; 

*At a certain distance below the earth's surface there is one unchanging temperature, and this 
is of the same degree as the mean temperature of the atmosphere of the surface. In northern 
Russia, where the mean temperature of the air is below the freezing point, the soil under ground 
is forever frozen, so that the wheat fields, say of northern Russia, ripen grain over forever frozen 
earth. At the north the permanent under-ground temperature is lower down below the surface 
than at the tropical regions. Contrariwise, the ocean-stratum of uniform warmth comes to the sur- 
face, in the far north and south, at the parallels of 60°. God, by these means, extends the range 
of the habitable parts of the earth by ameliorating the arctic and antarctic climates. 

| There are known periodical storms : in Europe in November and February ; on the coast of 
the United States in May and August. 

J The Atlantic monsoons off Africa and the Pacific monsoons off South America are on similarly 
shaped coasts. In the south-east of the state of Missouri (United States) there is a large area of 
land so low that it is often overflowed by the Mississippi. This area has been earthquake-rocked 
continuously for many months, and now remains earthquake ground. This area is also marked by 
frequent and intense tornadoes, leveling the trees of the forest. The volcanic island, Iceland, has 
few perfectly calm days, while fierce storms are common. During a devastating storm on a coast 
ol this island, it was calm twenty-seven miles off the coast, at sea. 

§The isothermals also run east and west over oceans unbroken by any large masses of land. 
The curves of the isothermals arc invariably over land, and the curves of equal magnetic variations 
bend over the lands. 



and also with variations of what is called barometrical pressure. In some 
tornadoes the wind is luminous with the force which it transfers; storms often 
exhibit most intense electrical phenomena. Is it then philosophical to cut off 
atmospheric commotions from the general dynamic phenomena, and to regard 
the wind as pacifying air disturbances only? 

The wind coming from the colder, north in some storms actually elevates 
the temperature as it advances station after station to the south. Often by 
night, when no wind blows, and when all other conditions of the weather are 
undisturbed, the thermometer will rise or fall many degrees. The ice of the 
Polar sea evaporates, and this at times when the air over it is motionless, 
while under the tropics, at times, no vapor ascends from the heated ocean.* 
Storms have one direction of advance, north, and in the opposite direction in 
the southern hemisphere. All these and other like phenomena have one solu- 
tion, the re-distribution of force; and this is sufficient to account for all the 
periodical weather-vicissitudes.-j- 

Theory of Storms. 

In this discussion the winter storms of JNTorth America will be mainly the 
subject of examination, the cause of these being the cause of all. The inves- 
tigations of the eminent meteorologist, Mr. Espy, show that very many of these 
storms commence east of the Rocky Mountains ; % that their axes are about 

*The received idea of precipitation, say that on a glass containing water, is that it is caused 
by avariation of temperature^ less in proportion to the dampness of the atmosphere. These are 
not cause and effect; the dampness of the atmosphere and the more ready precipitation are two 
phases of one condition. 

Evaporation is not from the temperature, nor from the blowing of the wind. These are often 
accompanying facts. Evaporation is hastened when the water is in an iron (conducting) vessel. 
It is hastened by connecting the water to the earth by a conducting wire. It is hastened, also, by 
the friction of the wind, which imparts force to the surface of the water. 

| The given rationale of the text also will account for the motion of "hug3 icebergs of the 
Arctic ocean, which, with tops up high in the air and with bases which, of course, extend far down 
into the depths of the ocean, rip their way through the surface ice and against a surface current." 
Whence comes their force, if not from the conversion of unseen planetary motion into divergent 
and visible motion? The independent planetary motion of parts of the earth is recognised in the 
Newtonian Astronomy, in the flux and reflux of the sea If the earth had not relative motion of 
its parts there would be " a horrid numbness" and an uninhabitable world. 

% There are also winter storms which rise over the land broken by the great American lakes. 


north-west and south-east; that these axes advance to the Atlantic coast, hold- 
ing themselves parallel ; that the minimum barometer is on these axes ; and 
that the wind blows in (often) on both sides of the advancing line. This 
direction of the storm-axis is coincident with a diagonal line of the continent, 
with the direction of the chain of the Apalachian mountains, and with the 
line of the Synchronous earthquake action. 

There is then, indisputably, a relation between these storms, trend of the 
coast, and line of earthquake-action.* 

The cause of storms has long been sought in the atmosphere. It is not 
there. The received opinion of unequal temperature of different altitudes of 
the atmosphere fails, because storm-winds are horizontal and close to the sur- 
face of the earth.-}- The advancing axis of a storm holds itself straight, mov- 
ing equably over the continent, which regularity is not the characteristic of air- 
disturbances. There must be then an inciting cause in the earth. Winds 
certainly re-distribute force. Therefore, by some cause, the earth requires 
additional force under storms. This cause is the elevation of the earth's surface. 
The presented rationale gives a unity to nature's acts, — the variations of the 
planetary velocity of parts of the earth being the ground of all dynamic phe- 
nomena,! * 

In the first place, it is a known fact that the level of the ocean rises under 
its storms, and that this elevation is before, and advances with, the progress of 
the storm. § 

* This lelation is also indicated by the general coincidence of volcanic and earthquake areas, 
and broken lands, with the birthplace of storms. 

| In one hundred balloon-ascensions the Mind of the higher altitude was found invariably to 
the eastward. It is so over the trade-winds. There have been winds so near the surface as to 
break the lower branahes of trees while the lofty branches were motionless. The upper region of 
the atmosphere is of the positive electric state. It is a fountain of force, and it impels the air 
in axial rotation, with greater velocity than that of the earth's surface. 

| Storms arise over volcanic areas and earthquake-ground, for here is the greater and more 
frequent relative motion of the earth's surface. 

§ li Storm waves and storm currents," (Johnston's Physical Atlas), " appear constant attend- 
ants on hurricanes. A storm wave is a mass of water of greater or less diameter raised above 
the usual level of the ocean, and is driven bodily along with the storm, or before it ; and when it 
reaches bays or river-mouths, or other confined situations, it causes dreadful inundations. The 



In the second place: Humboldt says that, ''without earthquakes the sur- 
face of the earth is capable of gentle and progressive undulations." It is 
known that vast areas of land do rise and fall year after year. Nature ever 
engrafts on the periodic, extensive, and secular movements, the minor, short- 
lived, and apj^arently fitful motions, as earthquake-motion accompanies the 
gradual upheaval of land. Thus, by fact as well as by analogy, the conclusion 
is reached, that there are storm-elevations of the earth's surface, which are so 
vast in area, — all around moving together, — that they are unseen and unfelt. 
only noted by the fall of the barometer, and by the rushing of the wind, freighted 
with force,* to be deposited on the rising portions of the earth, which have the 
orbit of axial rotation enlarged by upheaval. The cause of the trends of the 
coasts, the direction of the mountains and valleys, and the earthquake's range, 
thus coincide.-}- 

Humboldt says, it is impossible to believe that the breaking out of a vol- 
cano could disturb the equilibrium of the air all over Europe. The eruption 
and storm, are two phases of one act, to wit: — earth surface elevation, the 
friction and pressure of which, at the volcanic area, melted the rocks, and 
threw the lava forth, and which also caused the winds to blow and rains to 
•fall, for the redistribution of planetary force required by the elevation. 

"Whenever the surface of the earth rises at one place, there must needs be 
a depression at another, for the circles of latitude neither swell nor shrink on 
their whole circuit around the earth. Therefore, the mean of the reading of 
the barometer over one parallel, and also, of course, the mean of heat of the 

storm-currents may be briefly described as circular streams or the circumferences of rotary storms.'" 
Let it be here remembered that nature is always conformable to herself. An elevation of the level 
of water under a hurricane points out an elevation of the earth's surface under the storm's area. 
Storms usually have a more limited extent of synchronous action over oceans than over land. 
The former also have more of the character of winds in rotary storms. Recall the fact of the 
variation of the level of the great lakes usually followed by storms ; and of the river-bores and 
inundations of coasts, caused, unquestionably, by changes of the level of river or ocean-beds. 
Recall, also, the fact that the birth-place of storms is usually in broken land, archipelagoes, and 
volcanic and earthquake areas, which are also areas of changes of surface level. 

* T he air of certain storms is luminous with electricity. 

|Th6 Alleghanies were uplifted; and storm-elevations of the earth's surface, have their 
axes parallel to this chain, — nature repeating the same act in the same direction, and on the 
same earth-position. The increase of the flow of springs, and of the gas of coal mines, the 
ejection of water from earth-chasms before storms and so on, indicate the earth's surface-motions. 



whole parallel, is ever the same,— unusual cold and heat alternating on the 
parallels around the globe.* 

In earthquake and storm the barometer varies. The earthquake and 
storm and range of the barometer are not cause and effect, but are the visible 
effects or indications of a change of earth level. 

Whatever may be the hypothesis which is ultimately to be received, it 
will not be that which ascribes the fierce, lasting, and extensive air-commotions 
to minor air-disturbances. This is as unsound as if earthquake-action was 
imputed to the relative motion of parts of the earth's surface. The true theo- 
ries of meterology will unite the science with geography, geology and astronomy. 

The subject of oceanic currents will be briefly discussed: "The immense 
water of our globe," says Mr. Maury, "remains in equilibrium only by a never 
ending series of effort." Nature is a complete whole, and every part of the 
world is in harmonious relations w T ith the other part, — oceans, as mirrors, 
reflecting back the motions of the atmosphere. In the summer the trade- 
winds prevail further north, so also the gulf stream extends its flow more 
northwardly .f There are permanent winds and constant ocean-streams; there 
are periodic monsoons and periodic ocean-currents; there are sudden storms 
and fitful motions of the ocean-water; and, in many cases at least, the birth 
place of storms are where ocean streams commence their flow.J 

* For instance : an unusually cold winter diminishes the mean temperature on a parallel 
for the season: then from this mean, unusual heat increases gradually to its maximum ; and this 
alternation continues around the earth, generally in four mean and two maxima and minima; but 
the number of alternations vary. Temperature is clearly determined by altitude in mountains, 
and if so in this case, then in all. Thus the temperature of the summit of a mountain may vary 
from local causes, but the decrease of its temperature relatively to that of the base of the mountain 
is determined by relative altitude. So the variations of the temperature of one parallel preserve 
one mean year after year, because the surface of the earth cannot be elevated in one point without 
an accompanying depression elsewhere. 

f The gulf stream-belt of the diminished barometrical pressure follows the sun, as the trade- 
winds and tropical rainy seasons do. 

J" Here, "says Captain Porter, (U. S. N.), discussing the storms of the gulf stream, " we have 
every evidence that these gales exhibit their greatest violence in the gulf stream." Again, " Gales 
follow the gulf stream from the beginning to the end, at every curve." "Electrical phenomena 
is continually exhibited in one form or another." " The barometer invariably falls on entering 
this ocean river." The highest level of the water is near its axis, which is a ridge from which 
the water flows down each side. The gulf stream flows up hill only as water in passing out the 
mouth of a pitcher has less depth than the water over the bottom of the vessel 


It is admitted that the level of the beds or basins of the oceans rise and 
fall as do the dry lands of continents ; water is free to move to seek its true 
level: and of course there are ocean currents. 

These streams also act for its re-distribution. The force received on the 
commencement of their flow is imparted as heat (molecular motion) , as in the 
case of the gulf stream, or the streams part with it for unseen planetary 
motion, and are not heated by the friction of water. The oneness of the dyn- 
amics of the world is indeed beautiful ; and the idea that so much is accomp- 
lished, if not by one, by analogous action, is indeed wonderful.* 

* The gulf stream has its motion gradually slackened. The force giving the motion of its 
waters is transferred to the atmosphere, warming a large area. Beside a vast extent of ocean 
water, — lying far north and far east of its source, — is warmed. It is impossible, as has been said 
by an eminent meteorologist, that this stream can transport sufficient water, heated under the trop- 
ics, thus to fill with its warm waters the great extent of ocean which is known to be warmed 
because of the stream, as if branch streams flowed eastward (as has been supposed by some). 
It is fully demonstrated that the friction of water on water induces heat, this by direct 
experiment. There must needs be great friction in the moving of the water of the gulf stream 
against its water enclosures. If it be asked why the water on each side remains cool, the question 
can be readily answered : The force given off in these directions is absorbed for unseen planetary 
motion. There are cold ocean-streams, and such supply force for accelerating the planetary 
motion of parts of the earth. Ocean-streams have no authoritative rationale given by the 
schools. They are attributed to the blowing of the winds, to the greater heat of the tropical water, 
to the axial rotation of the earth, and sundry other causes. It may be depended upon (in the opin- 
ion of the author) that ocean-streams and atmospheric currents are from the same cause, and pro- 
duce analogous results ; therefore the key which opens the secret of one, will bring to light the 
secrets of the other ; for (again to repeat the truth) " Nature is simple in her operations, and always 
conformable to herself," 

M. de la Rives regrets that the influences of the ground on storms has not been heretofore 
better studied. He says, " It would be a great step in terrestrial physics to discover an intimate 
and decided connection between the geological nature of the ground and storms." " This con- 
nection," the author continues, " very probably exists." Mr. Dillwyn thinks that in mining coun- 
tries there are fewer storms than in other countries, and notably less than in calcareous countries. 

The connection between storms and internal earth-changes is also traced out by M. de la 
Rives : a fountain in long droughts, and even at times when it was perfectly dry, overflows when 
a storm is at hand. The flow of an Artesian well Was increased during a storm. In October, 1775, 
a sudden inundation caused immense ravages in most of the vallies of the Piedmont; and the 
disaster was preceded by horrible thunder ; much of the water of this inundation came out of the 
heart of a mouutain. Almost all Thermal Springs suffer a peculiar agitation on the approach of 
storms. An article of the transactions of the "American Association" proves the increase of the 



The Law of the Relative Motion of Parts of the Earth. 

It may be that more exact measurements and closer study will disprove 
some of these details of harmonious relations of the terrestrial masses ; but if 
half of these analogies and symmetrical relations of the earth's surface-divis- 
ions stand as facts, the position is established that law has determined the 
areas, contours, bearings and positions of earth-divisions, although in some 
cases the results of the law are not visible. Under what law is this symmetry 
determined? As the falling stone, a part of the earth, moves toward the 

rlow of springs in this country in advance of rains; so the increase of the oozing out of gas in 
coal mines fortells the coming storms. 

One significant fact was omitted in the text; an electrical discharge under certain circum- 
stances produces an agitation of air or wind. It is called, I think by Professor Leslie, the electric 
breath. In it the particles of air receive and transport the electric force, as is done by the winds 
of the earth on the great scale of action. 

The " electric wind" hastens the evaporation of liquids, and this, as has been proved by 
experiment, is not due to the renewal of the air over the surface of the liquid. This fact bears 
strongly in favor of the opinion given in the text on the subject of evaporation. 

.irrestation of Progressive Motion : Electricity, retarded in its progress, developes heat, "which 
heat, arises from, and is in proportion to, the resistance of the current." Electrical currents 
retarded in any liquid transfer, or give motion to, the liquid. 

Gulf Stream: M. Peclet has shown that heat, liberated by friction, always tends to give a 
less electric tension to that one of the rubbing bodies which is the least good conductor. The 
conductability of ocean water is in proportion to the degree of saltness. Does not the saltness of 
the gulf stream differ in degree from the saltness of its ocean banks? If so, then the constant 
atmospheric electric phenomena over the gulf stream is to restore the equilibrium. Another fact 
beats on this subject: Thermal electric effects not only take place at the point of contact but the 
electric current produces different-results, as it travels from the hot to the cold, or from the cold to 
the hot. 

Heat from retarded progressive motion: De la Rive says, " it is evident that the propogation 
oi heat is only a means of bringing about the molecular changes that give rise to electrical mani- 
festations, and that the propogation of electricity is, in its turn, only a means of producing mole- 
cular disturbances, which change the equilibrium of temperature. 

Floating Icebergs: A previous foot note refered to the motion of icebergs as planetary motion 
of parts of the earth. The author has since found that the direction of the motion of the icebergs 
of the north polar sea changes with the secular change of the variation of the magnetic needle. 




centre of the earth, by gravity, the force which determines for the earth its 
orbit of revolution around the sun, so the motion of the parts of the earth in 
upheaval and subsidence, and in horizontal motion, by which the relative 
positions and contours of the continents are determined, is also by a force 
acting under the law which moves the whole earth as a planet.* 

That, which gives the terrestrial masses, is the law by which the structure 
of the earth, geologically, is determined ; this is evident, for, on geological facts 
of upheaval the surface-structure of the earth, or the relief and contour of its 
surface-divisions, depend. It is believed by most eminent geologists-]- that the 
ultimate problem of what is called the upheaving force, which forms the relief 
and contour of continents, can only be solved by discovering its relation to the 
planetary force. This must be true, as the only difference is, that the one 
is in action on the whole earth, and the other, on separate portions or masses of 
the earth's crust. It is believed now by many geologists^ that the dislocation 
of strata, the uniform angle and long continued cleavage plane of rocks, and 
the parallelism of mountain chains of each geological era, and other facts of 
this character, show the action of a widely diffused and equably acting force, 
(Johnston's Physical Atlas), — a force which in countless ages has acted with 
the uniformity which attaches to the action of planetary force. The length 
of the major axes of continents of 138° arc, and the minor axes of continents 
of 84° arc, and the angle 30° of the trend of the coasts, and the bearing of 
so many world-wide apart islands and capes, are values calculated from 

*A11 things which exist in nature as a whole, are, at the same time, the parts of another whole. 
The vital principal of each is one ; the same vitality animates the universe, the one primitive 
power being revealed in divers parts, by divers degrees of perfection. 

f Not by all. Prof. Dana and other eminent geologists believe in a contraction of the earth's 
crust in cooling as the cause of the earth-structure. All seem to doubt an upheaval by an intense 
commotion of melted lava. Professor Dana asks, where does this force reside, and how does it 
act? What fills the void? Again this author says : " We must give up the popular idea (at least 
as a general thing), of the elevation of mountains by a force acting below, causing, at the time, an 
eruption of igneous matter. 

J No one has done so much to rescue the earth from cataclysms as Sir Charles Lyell. This 
eminent geologist is also a philosopher. He admits of no irregularities or catastrophes greater 
than now take place. He supposes that all things have remained from the beginning, subject to no 
greater change than they experience at the present time ; that geological causes have been the 
same in all ages, as nearly every rock found on our globe has been found in the process of, or 
course of, formation ; the processes now going on, being, in all cases, the same as those formerly 
in operation. 


23° 28' arc, which is the value of the obliquity of the ecliptic. If this result 
stood solitary and alone it might, with some show of reason, be regarded as a 
mere accidental coincidence. But it is far from being an isolated fact. This 
result is one of many facts of relationship of the structure of the world 
to its planetary elements, out of the very many Avhich are to be presented. 

If it were known or believed that the earth's structure has a relation to a 
planetary element of the earth, then a priori, it would be sought for in that of 
the obliquity of the ecliptic; for, the value of this flows from the position of 
the earth's axis, which places the orbits of axial rotation of parts of the earth 
oblique to the orbit of the revolution of the whole earth. The obliquity of 
the earth's axis being regarded as a primary fact, then the obliquity of the 
coasts to this axis is a derivative fact. 

The •Ellipticity of the Earth's Figure will now be discussed, as this throws 
light on the preceding subject. This figure is tin intermediate step, or fact, 
from the earth's surface-divisions to the earth as a planet. It is a fact of 
earth-structure, and also a fact pertaining to the whole earth as a planetary 
sphere. The value of the earth's ellipticity of form, or the measured excess of 
the equatorial over the polar diameter, is twenty-six miles and a fraction of a 
mile. How much labor has been expended to obtain this value by geodetic 
measurements ! Yet it is most directly derived from one measurement over 
the earth's surface, thus: The arc of earth's surface, 138°, was obtained from 
the obliquity of the ecliptic. It is the length of the major axes of the conti- 
nents and is, in difference of longitude, the breadth of many of the earth's 
surface-divisions; 138° arc (at 69.27 to an equatorial degree) is 9,600 miles : 
9,600 divided by 365.24+, (the number of the clays of the year,) gives as quo- 
tient 26.227 miles, which is the value of the ellipticity of the figure of the 
earth. Conversely, from the measured ellipticity of the earth, a governing 
measure of terrestrial masses, 138° arc can be calculated. 

This relation does not stand alone. It can be readily proved, by the 
result of another calculation, (as well as by theory,*) that there is a relation 

*The orbit of the earth's revolution is elliptical, and the orbit of the axial rotation of every 
atom of the earth is a modification of its orbit of revolution. The same characteristic which 
pertains to the whole orbit of revolution pertains also to its divisions into 365 cycloidal curves. 

For the young reader: Suppose a marked point on the periphery of a carriage- wheel ; this 
point (and every point of the wheel) rises and moves forward, then falls and moves forward ; this 
it repeats, and has one direction of motion in revolving and in progressing over die road ; it advan- 
ces in epicycloidal curves. 


between the elliptieity of the earth's orbit and the ellipticity of its figure, thus : 
The mean distance of the sun from the earth, as measured by the transit of 
Venus, 8.57+ parallax, to wit, 95,375,000, gives an orbit of 599,300,000 miles. 
Besides its orbital motion, the earth has a motion in space, by which the peri- 
helion of its orbit is revolved. The annual advance of this perihelion is 11.79" 
arc ; and, of course, the revolution of the perihelion is completed in 110,340 
years; Vto.Vtf of tlie earth's orbit, which is the annual velocity of its perihel- 
ion, is 5,450; TT i.^ T of this orbit, which is the daily velocity of the earth in 
its orbit, is 1,640,639 miles: then ti 5 t Vij T == tWj tllis > t&t of the earth's 
diameter, is 26.227 miles, which is the value of the ellipticity of the earth's 

To state this relation under another aspect: The period of the revolution 
of the perihelion of the earth's orbit is 110,340 years; the enlargement of the 
earth's circumference, by the ellipticity of its figure, is (26.227 X 3.1416 =) 
82.47 miles. Now, 110,340 times 82.47 equals 365.24 times the earth's mean 
circumference. This is thus calculated in diameter: 7,921 X 365.24 = 26.227 
X 110,340, the product of both multiplications being 2,893,877 miles. 

And under the third aspect: tWstV = iId which is the earth's ellipticity 
of figure, or ViW- This result is thus to be explained: -^i.zi of the period, 
110,340 years, is 302.1 years, equal to 110,340 days ; each year is -g-g-V.T °f sri-iT 
of the period; in -3 T ^. yT of the period (302.1 years) the equatorial excess or 
protuberance equals the diameter of the earth; in the whole period, 110,340 
years, the equatorial excess is repeated so as to amount to a motion equal to 
365.24 times the earth's diameter. 

That is, the "excess" adds 82.47 miles to the daily orbit of the earth's 
equator in axial rotation. In 110,340 days (302.1 years) there is an added 
motion equal to 365 times the earth's circumference. Then, the excess in the 
motion of revolution, once a year, in 110,340 years, (period of the sun's peri- 
gee) equals 365 times the earth's circumference. There is both an annual and 
daily "compensation" for the equatorial protuberance or excess. 

These harmonies are facts ; and, it is believed that no man of sound sense 
will call them "accidental facts." In the first place no such facts exist; and, 
secondly, the harmony between the ellipticity of the earth's figure and that 
of its orbit, is probable, a priori, because the symmetry of the cosmos is an 
extension of the symmetry of its parts. 

The ellipticity of 26.227 miles will now be calculated from other affiliated 
astronomical elements, which will fully demonstrate the correlations. The 
annual declination of the sun measured on the earth's surface, or twice the 


distance between the tropics, is 6,484 miles. This value is determined by what 
is called the obliquity of the ecliptic, and the magnitude of the earth. The 
fraction of a day in one tropical year is 0.242+ ; 0.242 arc of the earth's- cir- 
cumference is 6,034 miles ; this latter value is determined by the velocity of 
axial rotation and by the magnitude of the earth : and the magnitude of the 
earth is increased by its protuberant equator, or ellipticity of figure in diame- 
ter, 26.227 miles. Now, 6,484 (the first term) ■*■ 365.24 = 17.75; 6,034 (the 
second term) -^-365.24 = 16.53; the mean of these quotients is 17.14; the 
difference between 6,484 and 6,034 is 450; 450 -J- 17.14 = 26.227 miles. 

Let it be believed or not that the ellipticity of the earth's figure is because 
of the centrifugal force of axial rotation, this excess is of that value which brings 
this part of the earth into direct correlation with given astronomical elements 
of the earth ; and, it shows that the laws of planetary motion apply, under 
certain variations, to parts of the earth, as well as to the earth as a whole. 


The Hypothesis Derived from, or Founded upon, the Presented Facts. 

The rationale of the preceding facts cannot, in the limits assigned to this 
essay, be presented in detail. The leading idea only will be given ; and, it is 
clear, that a denial of the rationale of the author will not overthrow the facts 
of symmetry which have been set forth. 

What is symmetry? If we draw lines on a piece of paper, and, before 
the ink is dry, fold the paper in the middle of the random scratches of the 
pen, the lines will be repeated on the opposite side, and a symmetrical figure 
is the result; because, however irregular and confused were the lines as at 
first made, each line has imprinted itself opposite, and there ensues a balance 
of parts which constitutes symmetry. 

A symmetrical building has the same height, the same length, and the 
same finish and appendages on each side of the central line. The architect has 
repeated his work without a variation of plan; he has enlarged the edifice 


without a change of the original constructive idea. One part is wisely con- 
structed, and the wisely constructed whole is a repetition of perfect parts. It 
is, therefore, congruity resulting from unity of design which gives symmetry 
of structure. 

In the works of Nature this congruity and unity of design is exhibited in 
a most wonderful manner. We observe symmetry everywhere; as the Bible 
declares, "all things are double one against another." The limbs of an animal 
are duplicates ; its body on the one side of the medial line is the counterpart 
of the body on the other side; one animal is the type of another, of the same 
family. This congruity extends between families, races, classes, and orders of 
the animal kingdom. The animal fades away by an insensible gradation into 
the vegetable, and the vegetable, into the mineral kingdom. Element also 
corresponds to element, and this world itself, to other worlds; one division of 
the solar system, to another group of the same system ; and the solar system 
itself corresponds to the other systems of spheres which revolve around the 
great centre of the universe. There is no break in the creation — no disjointed 
members — no isolation of parts. One style or general character subdues the 
most varying into a common expression. Creation is an extension of divine 
wisdom; the most minute part is perfect, and the general perfection is a repe- 
tition of these perfect parts. Symmetry is, then, the many signatures of the 
one archetypal seal ; it is the participation of all things in the pervading and 
immutable wisdom of God. 

For an instance of this repetition of equal and alike parts : 109.62 times the 
moon's diameter is the moon's mean distance from the earth; 109.62 times the 
earth's is the sun's diameter; 109.62 times the sun's diameter is the mean dis- 
tance of the sun from the earth. It is almost, if not quite impossible, to con- 
sider these results as numerical accidents. 

The position has been assumed that parts of the earth have relative 
(special or individual) astronomical motion. The earth, therefore, must not 
be regarded altogether as a unity, if its astronomy is to be understood. This 
position is demonstrated if the measure, 109.62, applies to divisions of the 
earth's surface. 

The enlargement of the earth by its protuberant equator is 82.47 miles in 
circumference; 109,62 times 82.47 is 9,020 miles, or 130° equatorial arc. This 
is taken as one side of a right angled triangle. Make one of its angles 19° 47', 
as this is the obliquity of the magnetic, to the geographic equator, then the 
hypothenuse is 138° arc; 138° arc is the major, north and south, axis of the 
earth's continents, and 138° arc measures many east and west equal breadths 


of land, and of water, as is shewn on the map. Conversely, from 138° arc, the 
value of the ellipticity of the earth can be calculated by use of the value 

To apply this triangle to a special earth-position: The difference of lon- 
gitude of the west coast of South America, under the south, and of the cast 
coast of Arabia, under the north tropic, is 130°, or 109.62 times the ellipticity 
of the earth's figure; and the distance between the points, one under both 
tropics, is 138° ; and this arc rises 19° 47' oblique to the equator.* 

In the preceding statements of the symmetry, or correlation, of the ellip- 
ticity of the earth's figure, both the diameters and distances of moon, earth, 
and sun, prove the fact of the independent application of planetary laws to 
parts of the earth. 

Let now a fact be recalled, that both the earth's figure and its orbit are 
elliptical. The perigee of the orbit, that is, its ellipticity, revolves. Likewise, 
in symmetrical relation, the ellipticity of the earth's figure revolves. The periods 
of both revolutions are the same, to wit: 110,340 years. To the orbit of the 
earth, around the sun, there is an aphelion and a perihelion, and to the orbits 
of the earth's axial rotation there is an apcentron and a jpericentron. This 
must needs be, because, considering the ocean-surfaces, if continued around 
the earth, to constitute a true sphere, the more elevated land of one hemisphere 
constitutes an ellipticity of figure, which is so correlated to the ellipticity of 
orbit that the one, as has been shown, is calculable from the other. f 

* The arc of 138°, reaching from tropic to tropic, as described in the text, has very striking 
physical characteristics: continue this arc to a full circle around the earth, and it forms the sec- 
tion drawn on the south-east corner of the accompanying map. The arc (138°) commences on 
the west coast of South America, at a deep indentation of coast, it passes out of South America 
at a projection of the coast, it enters Africa at a concavity of coast, and exits at the projecting 
east cape of Arabia. The land under this line, 9,600 miles in extent, appears as if pushed to the 
eastward. The relief under this line has as strongly marked features as has the contour. In 
both continents the line traverses very lofty mountains, and highly elevated table-land, and it 
passes over a part of the Atlantic ocean, so shallow, that in some parts soundings have been ob- 
tained at 400 fathoms, — the bed of the ocean being mountainous. The line commences and ends 
in a volcanic and earthquake area. The line forms cotidal lines on both sides across the Atlantic. 
It is also on the magnetic equator, and so on. 

f The results of the measurements of arcs show that the earth's parallels of latitude (or orbit? 
of rotation) are not circles. [Trans. Roy. Soc] The arc measured in Asia shows a much less 
protuberance than those of Europe indicate. The earth has been measured for ellipticity on onr 
hemisphere only; and these results give great irregularity to its figure. 


This advance of the elevation of earth-surface is not by the translation of 
the solid matter. It is the progress of an elevation, or the propagation of a 
form, continuously, around the earth. 

The great elevation is divided into three parts, constituting the continents 
of America, Europe- Africa and Asia. 

The major axes of these continents are ever preserved 90° apart. 

The progress of the elevations is in an orbit inclined 19° 47' to the geo- 
graphic equator. 

The trends of the coasts are kept, approximately, at one angle with the 
meridian ; this angle (30°) being determined by or correlated to, the inclina- 
tion of the orbits of the axial rotation to the plane of the ecliptic. 

The obliquity of the orbit of the earth-wave, explains the obliquity of the 
magnetic equator and that of other meteorological curves. 

It explains the fact thus stated by Mr. Hitchcock : The present continents 
of our globe had for a long period constituted the bottom of the sea.* 

This hypothesis also 'gives the rationale of the varying direction of the 
mountain chains of different epochs, so clearly set forth by the eminent Elie 
De Beaumont in his pentagonal divisions (network) of the earth's surface. 

The mountains were raised by the lateral pressure, — remaining fixed in 
their elevation. Our hypothesis gives to geologists the lateral j>ressure which 
manifestly has accompanied upheaval ; as this is shown in the slaty cleavage- 
planes, in the upturning of earth-strata, and in their frequent interpenetration. 
It accounts for the facts traced out by Mr. W. D. Rogers, and which he attrib- 
utes to waves of fluid lava beneath the earth's crust, and it better explains 
these facts, as it dismisses the hypothesis of a "fiery furnace," which philoso- 
phers have long tolerated rather than believed. [See note appended to this 

The most primitive power of nature is not absolute; hence, there arises 
perturbations ; and, in the advance of the waves of elevation there must needs 
be some slight differences of the relative motions of parts of the earth. These 
perturbations produce volcanic and earthquake phenomena. For instance, a 
hindrance near Lisbon threw back a tremor on the line of the advancing earth- 

" Tout announce que le principal rriouvement qui survint a I'epoque de la formation des 
Andes arrive du cote de l'Ouest, c'est-a-dire, du cote ou une ligne d'escarpments qui marquent le 
rivage actuel de l'ocean depuis le Cap Horn jus'quaux Montaignes Rocheuse, continue a se sou- 
levre d'une maniere lente et a peine perceptible au mugissement et des bruits souterrain et sous 
I'influence des tremblements de terre repetes." 


wave; and an upheaval of any coast is marked by volcanic action, for then 
there is friction and pressure. 

A ship on the ocean, when struck by an earthquake is suddenly, and for 
a moment, impeded in its motion, as if it had struck upon a rock. The deck 
is the representation of earthquake phenomena on a small scale; loose articles 
are tossed about vertically and horizontally. A partial arrestation of the 
action of the upheaving force shows the same phenomena on the earth's sur- 
face; and the pressure created by upheaval is sufficient to account for melted 
lava and igneous rocks. 

The movement which transfers the earth's ellipticity of form around the 
earth in 110,340 years is indeed slow; and, like the growth of a tree, it i- 
unperceived. It is known that by it continents have been submerged and 
others relifted from the waters. The great movement is, as before said, gen- 
erally silent, peaceful and uniform; but at times slight perturbations cause 
apparent cataclysms ; these, the earthquake in its roar, and volcanoes in the 
issuing streams of lava, declare the existence and the regulated action of a 
power by which the planets revolve, as a ripple on the surface of a lake shows 
more distinctly, and brings out more palpably, the peaceful level of its waters. 

Although the presented hypothesis may not by niany be regarded as sound, 
still, as science looks higher and still higher in the heavens above, or pene- 
trates deeper and still deeper into the earth below, law, order and peace will 
extend their empires, and paroxysm and cataclysm be thrown away from the 
deep foundations of the world; and it may be hoped that the collected facts 
(apart from hypothesis) of this essay may aid the advance of science in this, 
its right direction ; for, no pJiilosojrfier can doubt for a moment, (though he may 
not comprehend how it is so), that every feature of the earth's surface is as 
normally found and placed, as is the earth's figure and position in its orbit : 
and, that what appears as paroxysmal cataclysms are acts of God, which pre- 
serve the normal position of the earth's surface divisions. 

It will be said that the earth's surface-structure and the geological posi- 
tion of its distorted strata show that once there was a more violent action of 
the upheaving force than now, this more violent action having been succeeded 
by an age of comparative repose. It is replied, that all things in nature sub- 
sist in continual change, and in perpetual growth. The earth itself has passed 
through various stages of advance, and is even now passing towards a greater 



maturity. All growth, or change of form, is from a relative motion of parts 
of which, the mass is composed. Geologists clescern indications of the progress 
or growth of this globe; from the beginning there is seen a gradual improve- 
ment "of our mansion house, the earth," in its bearings on the conditions of 
existence, from the earliest mineral and first cambrean zoophyte, until Mans' 
House was fully prepared for him. 

All unities are aggregations of other unities, as each individual organ of 
an animal has its independent existence, and discharges its special function. 
The atoms of a crystal, as if each had a separate life, cluster together in the 
normal form belonging to its chemical element. The crystals thus formed 
unite in the exact proportion, and in the exact relative position, by which a mass 
of hundreds of miles of granite is formed of the same colour, texture and 
hardness, so that a stone from one part is not distinguishable from a stone 
from another part of the quarry. This granite conforms in dip and strata to 
these elements extended over a whole continent; chains of mountains are thus 
formed parallel to the trend of the sea coasts; the angle of this trend is 
repeated all over the world; this angle is derived from the position of the 
earth's axis relatively to the plane of the earth's revolution; the orbit of the 
earth's revolution has its aphelion and perihelion; and the orbits of axial 
rotation have their aipcentron and jyericentron. These latter revolve as well as 
the former, and the revolution of the ellipticity of the earth's figure, in its 
repeated revolutions has been the instrument of Grod for the growth and better- 
ment of the world, rendering it the fit home of man. By each revolution a 
stratum, or a geological era, of the earth was formed ; and the primary solid 
foundations of the earth have been broken, softened and fitted to sustain ani- 
mal life of the highest order. Every succeding earth-wave as it rolls on cross- 
ploughs the surface, and there is less and less of what may be called paroxys- 
mal disturbance; and, therefore, it is true that ages of convulsion have pre- 
ceded this age of comparative repose. 

It is this revolution of the ellipticity of the earth's figure (as earth-waves) 
which has thrust up the mountains, the parallel chains being synchronous, as 
being uplifted by one special transit of the earth-waves. It is this which, by 
lateral action, or pressure, has protruded the capes and headlands into the seas. 
It is the oblique transit of the wave which gives the obliquity of metcrological 
curves to the parallels of latitude. It is this which has formed the cleavage 
plane of rocks, which has shattered the solid granite so that chemical action 
could more rapidly, out of the primitive strata, form the soil in which the 


life was to be; and thus by this action solidity and barreness are changed to an 
earth-surface on which annually the "green waves of vegetation"' flow from the 
equator towards the poles. 

Note. — In the text of this section, it is said that the fiery nucleus of the earth is an hypoth- 
esis tolerated rather than believed : perhaps this assertion is somewhat too strong. Yet there are 
so many objections to this hypothesis^ that the remark holds good as applied to many geologists of 
high intelligence. 

Volcanic phenomena cannot arise from the " fluid nucleous." Because, in that case the vol- 
canoes must be as holes down through the crust into the lava; and the ejecta of volcanoes must 
invariably be hot. Neither is the case. Cold and hot water, mud, sand, and even fishes are often 
thrown forth. Besides volcanoes are, as admitted by M. Prevost and other eminent geologists, 
themselves elevated as the lava is elevated by lateral pressure. It is supposed, by some, that this 
lateral pressure is from a contraction of the earth's crust, arising from cooling. It does not appear 
to ihe author a philosophical idea that God creates his worlds from melted lava, nor that worlds 
coutract, or expand, themselves into form ; but the idea that each atom of which the worlds are 
composed is placed under the same law which acts on the worlds as planets, appears to be a more 
beautiful, simple and logical conception. 

Let it be supposed that the earth was formed from melted lava: the lava must have been of 
one or of different specific gravities. If of one specific gravity, the consolidated matter would 
have remained of one gravity. If of different gravities, the lighter would have cooled on the 
surface; neither of which is the case. There are marks' of heat-fused rocks extending horizon- 
tally more than a hundred miles: if the central heat can melt horizontally, why does it not melt 
vertically up through the earth's crust? How could combustible matter be found in rocks? How 
could granite be formed, the constituent parts of which have differing points of fusion ? How 
could iron ore be found? as the heat would have changed the ore into cast iron, and this melted 
iron-ore has never been found. Some geologists place the melted matter only some twenty-live 
miles below the surface of the earth. To avoid the evils of this thin crust, some others place the 
fluid matter some thousand miles deep, thus throwing the evil further off; there are others who 
do not believe in the central nucleous, but suppose that the melted lava is confined in pools or 
reservoirs ; and there are many who have ho faith, whatever, in the existence of fiery furnaces, 
tolerating the hypothesis only because they need some deep seated force to give motion to the 
earth's crust. 


The Planetary Elements of the Earth in their Relations to each other. 

There are two primary motions of the earth, to wit: that of its axial rota- 
tion, which is completed daily, and that of its orbital revolution, which is com- 
pleted annually. The earth's orbit of revolution is changed by a motion of 
the earth by which the perihelion of its orbit is revolved; another motion of 
the earth modifies the form of its orbit by changing the value of its eccen- 

The axis of the earth changes its direction relatively to the ecliptic, or, in 
other words, to the plane of the revolution of the earth : first, its poles describe 
a circle in the heavens of 23° 28' radius, which is completed in 25,940 years, 
giving the precession of the equinoxes ; this circle of the precession is modified 
by another motion of the axis, completed in 18.6 years, giving the Nutation of 
the earth's Axis. Besides, the earth's axis has a secular change of its inclina- 
tion relatively to the ecliptic, which is, technically, the change of the obliquity. 
These minor motions of the earth, and of its axis, are the "equations" of 

There is, however, only one motion for each and every atom composing 
the earth, because it is impossible that any atom can move in two directions 
at one and the same time. The equations, therefore, are not isolated because 
of separate motions, but they are the visible phases of the one motion of the 
atoms composing the earth. The creation, as before said, is constituted as a 
perfect whole by the aggregation of perfect parts; the law of continuity 
extends from the organic to the unorganic creation, — to the surface -divisions of 
the world, — to its figure, — to the position of its axis, — to its position in its 
orbit. In the equations which modify earth-position, therefore, perfect harmony 
will be found, so that any one of these equations can be calculated from the 

As regards the Precession of the Equinoxes, it is said, (and the remark 

:;: " The creative spirit which broods ovei nature, and has clothed matter in the garb of time, 
not only confers on each special being ''(ens)" its special function and features, but links it in long 
and mysterious relationship to the others." — H. D. Rogers. 


will apply with more or less strength, to all the equations) : "Perhaps the solu- 
tion of no other problem has so often baffled the attempts of mathematicians 
as that of determining the precession of the equinoxes by the theory of grav- 
ity." [Trans. Royal Soc] Its value is therefore found by observation. Ob- 
servations before the day of Bradley are not reliable, and the period is now 
valued from observations of some hundred years back. These give an advance 
of the celestial equinoctial points of about 50.2" annually.* How easily and 
readily the value of the precession is calculated! 

The Precession of the Equinoxes: The earth's equatorial circumference 
being 24,937, and the orbit of the earth 599,300,000 miles, the linear value of 
the earth's circumference in arc of its orbit is 53.95"; the obliquity of the 
ecliptic is, say, 23° 28'; these are the only values needed for calculating the 
annual value of the Precession: 53.95" less 2 |ffo 8 ' of it (3.52") equals 50.43"; 
50.43" less 2 |^|o 8 ' of 3.52" (0.23") equals 50.20". By observation, the value is 
found to be from 50.1" to 50.2".f 

The Nutation of the Earth's Axis: This is a secondary motion of the 
earth's axis, it being a modification of the circle of the precession described by 
the poles of the earth. The primary motion of precession being 50.20" annu- 
ally, then: 2 -f|fl' of 50.20" equals 3.25"; deducting 0.21", which is 2 ^|l' of 
3.25", leaves 3.04" for the annual nutation of the axis. Erom more than eight 
hundred observations a value of what is called the major axis of the supposed 
ellipse of nutation of 17.955" was derived. [Ency. Brit.] This, as the diameter 

*The annus magnus of the ancients was 24,000 years, and the value of precession by them 
was taken as 54". 

This included the value of nutation, &c. Modern astronomers find, by observation, an 
irregularity of the motion of the equinoctial points ; the ancients discovered a trepidation in this 

The facts of the retrograde of the equinoctial points are thus illustrated; If a star is at the 
zenith of a point of the equator, for instance, at the begining of the year, at the end of the year 
it is not at the zenith by 50.2" arc, just as if the earth in 25,940 years made one retrograde rota- 
tion on its axis. It is accounted for, by the school, on the greater attraction of the sun and moon 
for the protuberant equatorial regions of the earth, which attraction is supposed to twist the earth 
completely around once in 25,940 years. 

fLaplace, " by a labored and profound process, gives to precession a theoretic value of 50.413". 
[Narien's Hist. Astron.]. Without entering into theoretic considerations, the simple calculation 
of the text gives the value of 50.20"; this needs a slight correction, to wit: a deduction of 
2' f o.25 = say .02, leaving 50.18" as the value; this is nearer to the result of observation 
than 50.4", — some observations giving a value as low as 50.1". 



of a circle, gives 56.4" for its orbit, or circumference. The circuit of nutation is 
completed in 18.6 years ; therefore, (56.4" -s- 18.6 ==) 3.04" is the annual motion, 
by observation. 

The Precession, 50.18", and Nutation, 3.04", are demonstrated to be in 
relation with themselves and with the obliquity of the ecliptic, thus : -/i? T \ 

= L_- L_ 4- 23°28' (ar\(\ m"> OTl^ — J - ' = 2 3° 2 8' 

16-5? 16-5 ' 360" V* 11 ^ DU VLi.) 15-34 ) 15-3 4 360°' 

The Change of the Obliquity of the Ecliptic: This equation is somewhat 
further removed from the preceding than they are from each other. A new 
element enters into its composition, or rather into the determination of its 
value, to wit: the eccentricity of the earth's orbit. 

The eccentricity of the earth's orbit is, say ^ of its diameter, or 3,220,000 
miles. The earth is nearer to the sun at perigee, and further off at apogee, 
than the mean distance, by 1,610,000 miles; dividing 1,610,000 by 24,034, the 
number of times the orbit contains the earth's circumference, gives as quotient 
67 miles. This is the diameter to a circle of the circumference of 210 miles : 

fllPll 210 - before produced i , i? Q£AO 4.^8" TllPValllA 

meil 57-9,Jijo,oo? - orbit of the earth aYFToYO - 0"0~ > 2",T~5"0~,"0 IT "5" Ui OUU U ^ UO • iUC VdlUB 

of this equation, by Bessel, is 0.456"; by Laplace, 0.462". 

Another method of finding the value of the annual change of the obliquity 
of the ecliptic is : The radius of the earth's orbit contains 109.62 sun-diameters. 
The precession is 50.18" annually: 50.18" - 109.62 = 0.457. 

And still another method: 2 -§^S' of the annual precession (50.18") is 
3.52"; and ^.^S'-fff?' of 3.52" equals 0.458. 

The Change in the Eccentricity of the Orbit: The division of the eccentricity 
of the orbit by the number of times the earth's circumference is contained in 
its orbit (see the second paragraph on the change of the obliquity of the eclip- 
tic) is 67 miles. This is diameter, the radius of which is 33.5 miles; 33.5 
miles is the annual change of the eccentricity of the orbit, (it is now becom- 
ing less) . The value of this change is not known exactly, either by received 
theory, or by observation. It is placed (Ency. Brit. Art Astron.) at 37 miles. 
Our theoretic deduction is 33.5 miles. 

The period and extent of the oscillation of the earth's axis constituting 
the Change of the Obliquity of the Ecliptic: Assume that the period of the 
oscillation is 24,034 years, which is the measure of the earth's orbit in earth- 
circumferences. The change being 0.457" annually, gives 3° 3* 27" as the 
maximum of the oscillation, or 1° 3V 43", from the mean on either side : then 

2^f.2 8 ' = the obliquity __ ,o 3 , /• 4 3 " = the oscillation 
3 60 =the circle 2 3°2f' = the present obliquity 

The value of the oscillation of the obliquity of the ecliptic is not exactly 
given, either by observation or received theory. Laplace assumes a value of 



1° 2V; Sir J. Herschel makes it less, that is, not more than 1° 21\ The theo- 
retic deduction of the author (1° 31' 43") is in excess of the received value by 
say some 10'. If it be correct, the maximum obliquity is 25° 58'; the mean, 
24° 2&; and the minimum, 22° 48*. The annual change is 0.45", and its period 
is 24,034 years. 

There are many methods of testing the correctness of these values, and 
the following is selected because of its simplicity : It will be remembered that 
the mean distance of the sun from the earth is 109.62 sun-diameters; and that 
this (109.62) multiplied by 3.332 gives, in its product, the number of days of 
the earth's year. The inclination of the sun's axis of rotation to the ecliptic 
is by observation 7° 20 v ; this (7° 20 1 ) multiplied by this ratio, 3.332, gives 24° 
26\ which is the mean obliquity of the earth's axis to the ecliptic as deduced 
from theory. 

Many of the discoveries of the author in this path of investigation will 
be omitted, as the facts already given suffice to show that as the earth's surface- 
divisions and its figure are related to the astronomical elements of the earth, 
so these astronomical elements are related to each other, forming a long chain 
of harmonious structure extending from the earth's surface to the heavens. 
These relations are presented as facts. The proximate cause of some at least 
of the equations, it is believed, is understood by the author, but the attention 
of the reader is directed to the Ultimate Cause. Very many instances of the 
same bearing of capes and head-lands of the earth's surface and of the sym- 
metry of the terrestrial masses, have been presented ; and many instances of 
the harmonious relations of the divisions of earth-surface to planetary ele- 
ments, of the earth's minor with its primary motions, and of the relations of 
these primary motions among themselves, have been proved to exist. Why 
do they exist? It is replied, that God's wisdom is perfect wisdom. And, 
being perfect, the same (cognate) results are repeated every where, — in every 
aggregation of parts ; in the tiny crystal, with its determinate angles ; in the 
persistent cleavage-plane of rocks ; in the one direction of the trends of coasts ; 
in the relations of continents to each other ; in the position of the earth's axis ; 
and in the position of the earth in its orbit; all being the symmetrical parts of 
a harmonious whole. 

Those facts in nature for which the cause can be assigned are, compara- 
tively, far down in the chain of mutual dependency ; the higher links being 
obscured by distance, the mind cannot rise up to them. How certain phenom- 
ena are dependent on each other, how interlaced, is beyond human wisdom. 
The highest reach of the mind is faith in God. Science in its ultimate soar 


becomes Theology, — the mind leaping from the known and calculable to those 
things concerning which these words only can be spoken : they are. 

The presented calculations of the earth's equations have one datum or 
element in all, to wit: the mean distance of the sun, or the value of earth's 
orbit relatively to its circumference: so, conversely, this fundamental element, 
the distance of the sun, or the radius of the earth's orbit, can be calculated 
from the observed value of the equations. For one instance of this: 50.18" 
(precession) j>lus 2 -f^|- 8 'of it, plus 2 |^|- 8 'of the former, and so on, gives 53.95". 
The earth's circumference is 53.95" arc of its orbit; and knowing the value 
of the earth's circumference, the linear value of 53.95" arc of the orbit is 
known, and of course the radius of the orbit is readily obtained. This gives 
for the orbit 599,300,000; for the radius of the orbit, 95,375,000 miles, equal 
to 24,034 times the earth's equatorial circumference, which answers, it will be 
remembered, to the horizontal parallax of the sun, as obtained by the transit 
of Venus, to wit: 8.57"; (this 8.57" being the radius of a circle of 53.95" circum- 
ference). The value of the sun's distance thus obtained from the value of 
precession, and that of the obliquity of the ecliptic, and so on, in the next 
section, will be demonstrated to be exactly correct by various other methods 
which give one common result. 

It will be remembered that the distance of the sun (to wit, 95,375,000 
miles) has been already determined, fractionally the same, from all. the earth's 
equations. This, a coincident or common result, takes the distance which is 
deduced away from the class of mere numerical accidents : Because, if so many 
balls as there are values used (representing these values) had been placed in 
an urn, and they had been withdrawn eight times, in the order which gave one 
value by analogous arithmetical processes, common sense (without any calcu- 
lation on the theory of probabilities) would declare that the balls were not 
placed in the urn hap-hazard. 

Note. A method for calculating the period of the precession of the equinoxes was acci- 
dentally omitted in the text. It will now be presented, as it shows the simplicity of astronomical 
phenomena, when they are stripped of their usual intricacy of statement. The precession of 
the equinoxes, in its value, depends on three elements: first, on the fraction of a day in a year 
over 365 days, = 0.242, and 0.242 arc of the earth's circumference is 6,034 miles ; second, on 
twice the distance between the earth's tropics, or on the annual declination of the sun as meas- 
ured on the earth's surface, which is 6,484 miles ; and third, on the number of times the earth's 
circumference is contained in the orbit, being 24,034 times, then: 6,034 -=- 24,034 = 0.251; 
"eiTaT^a T^To"- A y ear i s aTviTo" 0I " tne period of the precession of the equinoxea. 



The Mean Distance of the Sun from the Earth especially Discussed. 

" Croire tout deeouvert est une erreur profonde, 
C'est prendre l'horizon pour les bornea du monde." 

To obtain the distance of the sun from the earth with exactness is a great 
desideratum in astronomy. The problem has received the attention of astron- 
omers from the infancy of the science to the present day. Ptolemy and Coper- 
nicus thought this distance to be 1,200 semi-diameters of the earth (about 
5,000,000 miles) ; Kepler, 3,500; Ricciolus, 7,000, and so on. The received 
distance is 24,017 semi-diameters of the earth, equal to 95,375,000 miles. 

This value, says the eminent philosopher Dr. Young, [Nat. Philos., vol. 
2., p. 1.,] is generally supposed to be so far accurate that there is no proba- 
bility of an error more than one million of miles, or two millions at most, 
although some authors are still disposed to believe that the distance may be 
more than one hundred millions of miles. Leverrier speaks of great discor- 
dances in the measurements of this distance by different methods, amounting 
to one-fifth of the whole value. 

The received value is from observations of the sun's parallax. Parallax 
is the apparent displacement of an object as seen from different points of view. 
The object being seen in the direction of the visual ray, a change in the place 
of the observer changes the direction of the visual ray, as if the object itself 
had changed its own position while the spectator was at rest. 

For illustration: a tree is seen bearing directly west of the observer; if 
he then walk south, for say one mile, the tree will be seen north of west. If 
the tree is near at hand when first seen, it will be seen from the second 
station nearly north of the observer; if the tree were many miles distant 
from the first station, the change of its direction, as seen from the second sta- 
tion, would be comparatively slight, and it would be seen a little to the north of 
west. It will be thus understood that the degree of the change of position 
relatively to the observer depends on the distance ; and if this angle of change 
be measured, the base line (distance between the stations) being known, then 
the distance of the tree is easily calculable by a trigonometrical process. This 



change of the direction in which the sun is seen from two different stations on 
the earth is the solar parallax; and if the angle of change be measured and 
the distance between the stations be known, the distance of the sun can be 
readily calculated. 

The phrase, "the sun's equatorial horizontal parallax," has a technical 
meaning, viz: the difference between the position of the sun, as seen from the 
earth's equator, and the position in which it would be seen from the centre of 
the earth. This is a base of about 4,000 miles ; and the distance of the sun is 
comparatively immense. The angle subtending the base is therefore very 
acute, so that a slight error in the measure of it makes a very great error in 
the resulting distance. 

It is generally conceded that Dr. Halley's method of obtaining the solar 
parallax, by the transits of Venus across the sun's disc, is the most reliable. 
But these transits are of rare occurrence; the last was in 1769, and the next 
to take place will be in 1874. The received value of the solar parallax, 8.57", 
(distance therefrom being 95,375,000 miles) was derived from the transit of 
1769. Now, the observations of this transit are believed (as has been said) 
to afford a very accurate result, yet it is well known "that the results obtained 
by combining the observations at different stations, two and two, differ among 
themselves an entire second, equal to about one-eighth of the whole value. 
Therefore, the results by different astronomers vary. Muskelyne deduced 
from the observations, 8.72"; Short, 8 47"; Euler, 8.68"; Hornsby, 8.92"; and 
so on. The value 8.57" (now received) was fixed upon as a mean result of the 
observations supposed to be the most reliable. 

Recent observations on the method of Dr. G-erling (discussed by Prof. 
Gould, of Cambridge, Mass.,) give the solar parallax as 8.50"; what the limit 
of probable error is, has not been stated. 

"The diameter of the earth has served astronomy," says Herschel, in his 
Outlines of Astronomy, "as the base of a triangle in the trigonometrical survey 
of the solar system, by which to calculate the distance of the sun, but the 
extreme minuteness of the sun's parallax renders the calculation from this 'ill 
conditioned' triangle so delicate that nothing but the fortunate combination of 
favorable circumstances afforded in the transits of Venus can render the result 
even tolerably worthy of reliance. 

The determination of the solar parallax rests, thus far, solely on its meas- 
urement with the short base of the distance between two earth-stations of 
observation. And, however perfect the instruments of observation, and how- 
ever great the skill in the use of them, as has been said, the solar parallax 


cannot thus be measured reliably within some fraction of a second, and a small 
fraction of a second varies the distance a million of miles. 

But, on the other hand, it is believed that astronomers are not necessarily 
confined to the measurements of the required angle subtending the distance 
between two earth-stations as a base, and that the distance of the sun can be 
determined by the value of certain periods, as will be shown. But how, it 
will be asked, can such methods exist, when astronomers of the most acute 
minds, and very thorough mathematicians, with the aid of most extensive learn- 
ing, have failed to discover them? "Astronomers," says Leverrier, "have 
encountered dangers, journeys, suffering and almost martyrdom itself, to 
determine this fundamental element of the solar system." Is it possible that 
a method which a youth can comprehend, and to which school-boy mathematics 
can apply, will answer this great question satisfactorily, — working out a prob- 
lem which has baffled all astronomers? 

These astronomers, it is replied, are educated in the most abstruse theories, 
and to apply these theories by the most abstruse mathematics. Abstruse 
theories and abstruse methods are apt to hide simple truths; and the eye, con- 
tinually strained to see afar off, is unfitted to observe objects near at hand. 
Besides, they all have sought in the same direction. And they have been too 
intently engaged in the process to seek other methods of solving the question. 
Therefore, many simple methods may exist, and have been undiscovered by 

There is assumed as the mean distance of the earth from the sun, a value 
of 95,375,000 miles, — the mile being T ,gVr of the earth's equatorial diameter. 
This distance in sun-diameters (of 870,107 miles), as integer of measure, is 
109.62; in earth-diameters (of 7,937 miles), 12,017; in radii of the moon's 
orbit around the earth (of 237,319 miles), 401.87. This value, which, in the 
preceeding section, was proved to be conversely calculable by six different 
methods, is now the subject of s]Decial discussion, and of direct calculation. 

To commence with the seventh method, the formula of which is : The cube 
root of the square of the product of the earth's solar days of periodic time 
multiplied by the ratio of the diameter to the circumference of a circle, equals 
the earth's distance expressed in sun-diameters. Thus: 365.24 (period) X 
3.1416 (ratio &c.) = 1,148; the square of 1,148 = 1,316,700; the cube root 
of 1,316,700 = 109.62, which is the number of the sun-diameters contained in 
the assumed distance; and, in like manner, in case of each one of the planets, 
its distance is calculable from its periodic time. 


By Kepler's law, the greatest and most original discovery of the moderns, 
the cubes of the distances of the planets are to each other, respectively, as are 
the squares of their periodic times. The result obtained by this law, is the 
ratio of planetary distances, or the relative distances of the planets. Thus, 
if the earth, with its period, has a certain distance, then the planet Venus has 
a distance calculable, in conformity to the law. To obtain the positive distances 
of any one of the planets, by Kepler's law, requires that the distance of one 
planet be observed, or be derived from actual measurement. It can do nothing 
positively, without a measured distance. The earth's distance can be measured 
by far the most reliably. Hence the importance of this element ; because, upon 
its value, the values of the distances given to all the planets respectively, and 
the value of the amplitude of the solar system itself, depend. The formula 
of the author, agreeing, in its result, with the distance derived from observa- 
tions, gives, not only the positive distance of the earth, but also the positive 
distances of each one of the planets by itself, and as if the one planet only 
existed. And, while no measurement whatever is required to give the distance 
in sun-diameters, even to arrive at the distance in miles there is no necessity 
of measuring the diameter of the sun, as the value of the sun's diameter is 
the subject of calculation from other and more easily and reliably measurable 
elements, as will be afterwards fully explained. 

This method of the author's was first published in 1852. It measures 
distance in the natural and philosophical integer of its measure, — the diameter 
of the central luminary. Its integer of measure for the period is likewise the 
natural and philosophical integer of time, because the period of the earth's 
solar day is derived directly from certain elements of the sun, as, in the sequel, 
will be shown. 

The eighth method is from the symmetrical construction of the solar sys- 
tem, — God repeating every where the same measure, in determining the 
diameters and the distances of the spheres. The mean distance of the earth 
from the sun bears the same ratio to the diameter of the sun as the diameter 
of the sun bears to the diameter of the earth ; and as the moon's mean distance 
from the earth bears to the moon's diameter. 

Let it be supposed that this threefold repetition of the foregoing ratio, 
109.62, is "a mere numerical coincidence," then what is to be believed of the 
following? The ratio of the moon's diameter to the diameter of the sun, (plus 
one moon-diameter), 402, is the same as the ratio between the moon's mean 
distance from the earth and its mean distance from the sun; and also as the 


diameter of the earth to the eccentricity of the earth's orbit. There are two 
ratios each of threefold repetition attaching to the same values ; and thus, by 
inter-relation exhibiting faultless symmetry of construction. 

In the ninth method the value sought is obtained through the values of 
the magnitude of the sun and the value of the velocity of its axial rotation. 
The diameter of the sun, by observation, is 880,167 miles. Its value without 
its luminous envelope, or effulgent atmosphere, is assumed to be 870,167 miles. 
The value of the sun's period of axial rotation, as given by different observa- 
tions, varies to a greater extent than one-quarter of a day; the mean of many 
observations is 25.25 days. It is assumed to be 25.212 da} r s, and these two 
values, of the magnitude and axial period of the sun, thus assumed on theo- 
retic considerations, will be demonstrated to be the true actual values in the 
progress of this discussion. These values give to the sun a daily equatorial 
axial velocity of 108,900 miles. 

Now let a planet be supposed to exist the period of the revolution of 
which equals the period of the sun's axial rotation, to wit, 25.212 days. On 
the assumption that the earth, with a period of revolution of 365.24 days, has 
a distance of 109.62, then, the supposed planet of 25.212 days period of revo- 
lution has a distance of 18.45 sun-diameters. The latter, the fictitious planet, 
would have a daily velocity of 4,014,000 miles. Its orbit would be 36.89 times 
the sun's circumference ; and 4,014,000 -*- 36.89 = 108,900 miles. Thus, the 
planet of 25.212 days period is shown to have 36.89 times the velocity of the 
sun's equator in axial rotation ; the orbit of the planet being 36.89 times the 
equatorial circumference of the sun; therefore, the velocity of the planet is 
increased, outwardly from the sun, in simple proportion to the distance; or, in 
other words, the angular velocity of the planet in its orbit is the same as that 
of the sun's equatorial circumference in axial rotation, which is not the case 
with a planet of any other distance. On our assumption, therefore, that the 
earth's distance is 109.62 sun-diameters, and the period of the sun's axial 
rotation is 25.212 days, a fictitious orbit is traced out in the heavens, in which 
the axial rotation of the sun and the velocity of the orbital revolution of the 
planets meet as if one value. 

This orbit of 18.45 sun-diameters radius is a cosmical or fundamental 
planetary orbit.* And, by the determination of this orbit the sun appears as 

* The cosmical hypothesis of the great Swedenborg is that the planets are derived from 
a solar or cosmical sphere or ring on the ecliptic. Billion's hypothesis is a bad version of 
Swedenborg's. Of the Laplace nebular hypothesis Sir John Her sch e] says : " If it is to he regarded 
as a demonstrative truth or as receiving the smallest support from any observed numerical 
relations which actually hold good among the clement; of planetary orbits, 1 beg leave to demur." 



if left orbitless and alone, at the centre of the solar system, not only to throw- 
light over its encircling worlds but also by its magnitude and axial velocity to 
give that light to the human mind by which the structure of the solar system 
is to be discovered. 

Tenth method : The fundamental planetary orbit has a radius of 18.45 sun- 
diameters : 18.45- "I (for the sun itself) = 17.45 ; 1745 X 2 = 34.89 ; 34.89 x 
3.1416 (the ratio of the circumference to the diameters of a circle) = 109.62, 
which is its distance of the earth from the sun in sun-diameters as the integer 
of measurement. 

Eleventh method: 34.89 (preceding paragraph) + 3.1416 = 11.10; the 
squareroot of 11.10 is 3.332 ; 365.24 (the number of the clays of a year) h- 
3.332=109.62 ; thus again the distance of the earth from the sun in sun-diame- 
ters, is reached. 

Twelfth method: Let the diameter of the earth's orbit be measured in the 
number of the days of the orbital velocity of the earth ; then, the orbit being as 
365.24, it follows that (365.24 -- 3.1416 = ) 116 is the measure of the diame- 
ter of the orbit; 116 -*- 3.1416 == say, 36.89, which is the number of sun-cir- 
cumferences contained in the fundamental orbit of a planet of 25.212 clays pe- 
riodic time. 

Thirteenth method : 36.89 (preceding paragraph) less t °f & (exclu- 
ding the sun which is T¥ 1 TT of the radius of the fundamental orbit) is 34.9 ; 
34.9 -*- 34.89 divided by 3.1416 equals 11.10; 11.10 X 65.8) which is the ratio 
of the earth's orbital to its equatorial axial velocity = 730.5 ; one half of which, 
365.24 ; is the number of the days of the earth's year. This result, the num- 
ber of the days of the year, is reached by 65.8, as an intermediate term ; 
and, on the assumed distance of the earth from the sun, the ratio between 
the earth's orbital and its axial equatorial velocity is 65.8. 

The preceding methods (from the ninth inclusive) furnish a foundation 
for the true cosmical relations of the earth and sun. 

Fourteenth method : This may be lightly regarded, at its first view at least, 
by astronomers, because the method is founded on a very ancient astronomy. 

" Thus the earth and heavens were finished, and all the hosts of them. 
And on the seventh day God ended His works which He had made ; and He 
rested on the seventh day and hallowed it." Thus saith the Bible, and on this, 
the septenary division of time is based by the Scriptures. An assumed ficti- 
tious planet having six solar days of periodic time without any fraction of day, 
would have seven times the sum of the sun's, the earth's, and moon's diameters 
also without a fraction. The sun's diameter, 870,167, plus the earth's, 7,937, 


plus the moon's, 2,160, equals 880,264 miles. By Kepler's law, the earth of 
365.24 days period having a distance of 95,375,000, a planet of six days period 
would have a distance of 6,161,848, Avhich is seven times 880,264 miles. 

Are there not other indications of a seven-day structure of the heavens 
and earth? The earth's distance is 109.62 sun-diameters; 109.62 -*■ seven = 
15.66; 15.66 less 0.5 (for a semi-diameter or radius of the sun, because the 
calculation is from the Sim's surface, not from its centre,) gives 15.16 The 
earth's orbital velocity is 15.16 times that of the axial equatorial velocity of 
the sun ; that is, the earth's orbital, is increased outward from the sun's axial 
velocity in a seven-fold ratio. 

Again : The ratio of the number of the sun-diameters of its distance from 
the earth (109.62) to the number of the days in a year (365.24) is 3.332; 
3.332 x seven = 23.32 ; 23.32 x 2,160 (the moon's diameter is 2,160 miles,) 
== 50,400 miles which is the daily velocity of the moon in its orbit around the 

And again: The sum of the earth's and moon's diameter (7,937 and 
2,160) is 10,097 miles: seven times of which is 70,679; less t °f i* ( as the 
sun has 14.49 rotations in one year,) and the sum is 75,556 ; 75,556 X 3.1416 
== 237,319 miles, which is the mean distance of the moon from the earth. 

Once further : To the value 75,556 (of the preceding section) add ^ 
(as the lunation is completed in 29.53 days or rotations of the earth), and the 
sum is 78,109; 78,109 -*- 3.1416 = say 24,920 miles which is the mean cir- 
cumference of the earth. 

These instances indicate a seven-fold structure of the heavens and the 
earth ; and whatever may be thought of the origin of the septenary or heb- 
domadal division of time, it is a fact that a planet of six days period has a dis- 
tance of seven times 880,264 miles, which is the observed diameter of the sun. 
(See note appended to this section.) 

The fifteenth method is simple and direct, and, taken into consideration 
with the method next following, opens to view certain fundamental laws of the 
structure of the heavens. Why has the moon 29.93 earth-diameters of mean 
distance from the earth and only 29.53 days as its lunation or synodic period ? 
There has been no attempt even by astronomers, to answer this question. — al- 
though the true answer declares the distance of the earth from the sun. The 
difference between 29.98 and 29.53 is J. T . T of 29.98 ; and the earth's equatorial 
axial, is -J-j.s of its orbital velocity ; this holds good on the fact that the earth is 
distant from the sun 95,375,000 miles as assumed. The moon has not any axial 
rotation, and therefore, as the complement or equivalent, the moon has its ve- 


locity in its orbit around the earth, so much increased ( t l_ part) so that the 
lunation has a less number of days than it has of earth-diameters of distance :; 
because what may be called the normal period of the moon in her orbit around 
the earth is as many days as it has earth -diameters of distance, — one day 
for each and every earth- diameter of distances. 

The moon, it is true, has, as have all other revolving spheres, a quasi or 
sidereal rotation completed once in a revolution around the earth. This rota- 
tion is not a motion superadded to that of revolution, but the sidereal rotation 
flows from, is in consquence of, and ever from necessity accompanies, the mo- 
tion of revolution. This kind of rotation is easily explained. The moon re- 
volves around the earth keeping one hemisphere, (libration excepted) directed 
towards the earth, and this because the moon does not turn around or axialy 
rotate. In revolving around the earth, the part of the moon the furthest from 
the earth has an orbit larger than the orbit of the moon's centre by the moon's 
circumference. Hence the moon may be said to have axial rotation, because 
that part of the circumference of the moon which is the farthest from the earth 
has a greater velocity of orbital revolution, than the orbital velocity of the centre 
of the moon, by one circumference of the moon. But not a particle of the moon,, 
in attaining to this result, has any other motion than that of revolving around 
the earth : therefore, while it may be truly said that the moon has mathematical 
rotation, it cannot be truly said it has si physical or actual rotation on an axis 
within itself, — its surface does not turn around upon a centre or axis of the 
moon within the moon. 

For an illustration : a circular saw rotates on its axis, the teeth of the saw 
keeping their bases directed to the centre of the saw's motion. Now the moon in 
revolving around the earth keeping one hemisphere directed to the centre of its 
revolution, rotates on its axis no more, nor less than, but exactly as the teeth of 
the circular saw turn on special and individual axes once in a revolution of the saw! 
This is the only kind of axial rotation which the moon has, as was admitted by 
Dr. Lardner, who was one of the champions in the long and sometimes angry 
discussion of this subject in England, — the learned doctor being on the side of 
those who contend that the moon has axial rotation ; but he averred that the 
text books on astronomy did not explain the idea to the public ; and in this 
respect he did not appear to-be more successful. 

Sixteenth method : In the preceding; the distance of the earth from the sun 
was found, by the difference between the (nil) axial rotation of the moon and 
the value of the earth's actual rotation, which results in the fact that the revo- 
lution of the moon around the earth is completed in a less number of days 


than there are earth-diameters in the distance of the moon, — the greater orbital 
velocity of the moon offsetting its lack of rotation. The earth's distance from 
the sun being 109.62 sun-diameters, why then it may be asked according to the 
law, — a rotation for each diameter of the primary contained in the distance, — 
has not the earth 109.62, in place of 365 rotations ? This, it is answered, is 
because of the fact that the ratio of the sun's equatorial axial velocity (the sun 
being as the earth's primary) is 4.34 + times that of the earth's. The sun has 
14.49 + periods of rotation in a year; 14.49 -^-4.34 + = 3.332; now, what 
may be called the earth's normal (or cosmical) number of rotations, — 109.62, 
(one rotation for each and every snn-cliameter of the distance of the earth 
from the sun,) multiplied by 3.332, gives 365.24, — which is the actual num- 
ber of the earth's rotations in one year. Conversely, the distance of the 
earth from the sun in sun- diameters can be calculated by its number of clays of 
periodic time. 

The Seventeenth method still further developes the harmonious (cosmical) 
relation previously set forth. The ratio between the earth's orbital and its 
axial equatorial velocities is 65.8; T 4.-g- of the moon's orbit (1,491,600) is 
22,643 miles. The distance of the earth from the sun is 402 times the radius 
of the moon's orbit around the earth : Now, 402 times 22,640 miles (-g^ olthe 
moon's orbit) equals 365.24 times the earth's circumference, which is the annual 
axial velocity of the earth's equator ; any other distance would change the term 
-g-i-.-g- and this harmonious result would not be produced. 

Eighteenth method : The earth's axial equatorial velocity is T i. T of its 
velocity in its orbit around the sun. Assume that the moon has axial rotation, 
to such an extent that its equatorial surface has a velocity in every lunation of 
_x_ of the velocity of the whole moon in its orbit around the earth. In that 
case the equatorial axial velocity of the moon would be 22,643 miles in each 
lunation. This is 3.332 times the moon's circumference. Therefore, had the 
moon an axial rotation of the velocity of T \. T of its orbit around the earth (as 
the earth has an axial velocity of T |. T of its velocity around the sun), the moon 
would rotate as many times in one lunation as the earth rotates for each and 
every sun-diameter in its distance from the sun. And what is truly significant, 
the moon would rotate in the period of the revolution of the perigee of its orbit 
365.24 times, that is in that period (revolution of the moon's perigee), the moon 
would rotate as many times as the earth rotates in one of its revolutions around 
the sun. 

The Nineteenth method is omitted simply because to unfold the idea clear- 
ly would require more space than can be used and preserve the assigned limit 


of this Essay. It is founded on an oscillation of the sun's perigee (which was 
discovered in the discussion of the solar tables by M. Leverrier,) which 
oscillation is completed in 661 years, according to the calculations of this emi- 
nent astronomer. Its period is 65.8 years, — according to our theory, — which is 
the ratio of the earth's orbital to its equatorial axial velocity. In 65.8 years 
the velocity of a point of the earth's equator in axial rotation equals the annual 
velocity of the earth in its orbit.* 

Twentieth method: The fraction of a day in one year is 0.242 of a clay, 
equal to T ^ T of a year. The daily velocity of the earth in its orbit is 1,640,639, 
and the value of this orbit is 599,300,000 miles ; now, from these elements as 
data it is required to know what is the fraction of a lunation in one year over 
twelve whole lunations ? 

i,5oo _ i 1 6 4 o,L39_Hj,3oo,ojo i j^ is 551.000 miles (the moon's orbit 

I 1 » 8 8 5 5 1 1 O * \ 

being 1,491,600 miles) = 0.369 arc of the moon's orbit. Thus directly this frac- 
tion of a lunation is calculable from the fraction of a day in a year over 365 ; 
and this, through the assumed distance of the earth from the sun, (giving the 
value of the orbit as 599,300,000 miles), as the intermediate term. Therefore the 
assumed distance is the true distance. So conversely, the fraction of a day can be 
calculated from the fraction of a lunation in a year ; and the distance of the earth 
from the sun from either term. This method alone is sufficient to solve the 
problem under discussion. 

It is stated in Whewell's history of the "Inductive Sciences" that no reason 
has or can be given why the earth should turn on its axis 365 and not 300 or 
400, or some other number of times in a year. It is strange that astronomers 
should rest content with this ignorance, willing to place the value of the day for 
so long a time in the chapter of accidents, — among those things for which no ra- 
tionale is assigned. It has been shown in the fifteenth and sixteenth methods 
of this section, that the number of lunations and the number of days in one 
year are, most truly, be in strict relation to the distance of the moon and earth 
respectively from their primaries, — the earth being as primary to the moon, and 
the sun as primary to the earth. 

The attention of the reader is especially requested to the following, — the 
twenty-second method, — for the following reasons : The converse of the process 

•The midnight part of the earth's equator has a greater orbital velocity relatively to the sun; 
than its noon-part by, annually, say 50,000 miles. Thus, in consequence of this, the diameter of the 
sun at noon, as measured by its arc of apparent motion, is the largest ; and from the extent of this noon- 
day enlargement the distance of the sun from the earth can be calculated. 


will give the values of the diameter of the sun, and the value of its period of 
axial rotation. This is important, because, by the glare or effulgence of the sun, 
its diameter cannot be measured reliably within some ten thousand miles; and 
its period, because, the spots or maculae by which the velocity of the sun's ro- 
tation is observed have a proper motion, or a motion independent of the sun's 
surface, cannot be measured reliably within a quarter of a day. Secondly, be- 
cause the method is simple and direct, and by itself determines the problem 
under discussion : Divide the number of days in the earth's tropical year, to 
wit, 365.24, by the ratio of the sun's to the earth's equatorial axial velocity to 
wit, 4.34, and the quotient is 84, then f f-; 2 > 2 = ¥ .j n . * This ratio 3.332 to 1, 
as before shown, is as 365.24 (days of the year) to 109.62 (the number of the 
sun-diameters contained in the value of the distance sought in this discussion.) 
But also, 3.332 X 3.1416 (the ratio of the circumference to the diameter of a 
circle) = 10.47. This, 10.47, is the number of times of the annual velocity 
of the earth's equator in axial rotation (or 365.24 times the equatorial circum- 
ference of our globe), in 95,375,000 miles which is the radius of the earth's orbit 
or the mean distance of the earth from the sun. 

Twenty-third method: A point on the earth's equator has an annual ve- 
locity of, or moves through, 9,107,990 miles in a year. The mean distance of 
the moon from the sun (equal to the earth's mean distance from the sun) is 401.87 
times that of the mean distance of the moon from the earth, and 65.8 is the ra- 
tio of the earth's axial equatorial to its orbital velocity: Now 9,107,990 (as 
before given) -*- 401.87 = 22,643 miles which is T -j^ of the value of the moon's 
orbit around the earth or 1,490,600 miles. This method presents certain before 
given harmonious relation under a new aspect. 

The twenty-fourth method is, indeed, simple: The fraction of a lunation 
in the year, over twelve whole lunations, is 0.369 of a lunation. This, in time, 
as measured by the mean velocity of the earth in its orbit is 3V.T2 °f a year. 
Divide -3-5,-52 hy 12 (for the twelve whole lunations) and the quotient is ^J^ 
this, 401.88, is the number of times that the radius of the moon's orbit around 
the earth is contained in the radius of the earth's orbit around the sun, o-ivinar 
95,375,000 miles as the result of the problem, which is to find the mean distance 
of the earth from the sun. . 

The twenty-fifth method, in its converse use, gives the value of the eccen- 
tricities of the earth's orbit : 402.23 as the multiplier of the moon's diameter 
produces, as product, the diameter of the sun (plus one moon -diameter) ; 402.23, 
(401-88) as the multiplier of the radius of the moon's orbit around the earth 

* The sun's period of axial rotation is 25.212 days. 


produces the mean distance of the moon from the sun ; 402.23 times T ± T of the 
moon's orbit is equal to 365.24 times the earth's circumference. And, to extend 
still further the use of this ratio : 402.23 as the multiplier of the earth's diam- 
eter gives, in product, the value of the eccentricity of the earth's orbit, (thus, 
7,937-the earth's circumference, x 402.23 = 3,190,500; tW.ttt.^t SSSf' 
— _i__ Tr which is the excentricity of the earth's orbit. Conversely, the mean 
distance of the earth from the sun can be calculated. 

It appears at first sight as if the relative diameters of the planets and the 
relative amplitudes of their orbits, are without rule or order. The pigmy 
planet Mercury is the nearest to the sun, — a great central sphere of nearly a 
million of miles of diameter; then come Venus and the Earth, equal sized, and 
of about double of the magnitude of Mercury ; then, there is Mars, of about 
one half the size of the earth. Between Mars and Jupiter are placed the toy 
planets, as they may be called, the asteroids, which, as a family of Lilliputian 
worlds, sweep around the sun in beautifully interlaced orbits, — many of them 
being so small that the telescope is required to enlarge them into visible worlds ; 
Jupiter is ten times as large as the earth is ; and the ring-encircled Saturn is next 
to, and about as large as, Jupiter ; after Saturn, Uranus is found, of less mag- 
nitude than Saturn ; and smaller still is Neptime, which presents itself as the 
TJtina Thule of the system. Besides this irregular sequence of difference of 
size, the received philosophy makes one of the spheres of the system as light as- 
cork, and others of varying densities, down to a sphere which is heavy as lead. 
Then, Mercury, Venus, and Mars have their periods of axial rotation about 
equal to that of the earth's, while the rotary velocity of Jupiter is, say, thirty 
times greater. And further still : there is no rationale given for the variations 
of the eccentricities of the planetary orbits, nor for the varying values of their 
axial inclinations. 

So far, however, as relates to the diameters, the distances, and the periods 
of rotation of the sun, the earth, and the moon, and to the inclinations of the axes 
' of the sun and the earth, and to the eccentricity of the orbit of the earth, a harmony 
of relation has been set forth, so that any one of these elements is calculable 
from the other elements. To recapitulate a few instances of this : the distance 
of the earth from the sun measured in the radii of the moon's orbit around the 
earth, as the integer of measure, furnishes the ratio between the earth's diame- 
ter and the eccentricity of its orbit ; also, the ratio between the sun-diameters 
contained in the earth's distance to the number of the days of the year, is also 
the ratio of the inclination of the sun's axis of rotation to the mean inclination 
of the earth's axis ; and again, there is one of the diameters and the distances 


of these three spheres which is found to be of three fold, and another ratio to 
be of four fold application. It is not necessary to recapitulate a greater num- 
ber of these harmonious relations in order to show, most conclusively, that so far 
as the astronomical elements of these three spheres are concerned that they are 
determined by law ; and that chance, accident, or fortuitous happenings had 
naught to do with their velocities, magnitudes or distances. 

The sun is apparently at a distance so immense that it appears impossible, 
especially to the uneducated, that the measure of the vast extent of this space 
between our globe and the central luminary can be known. The author re- 
members to have heard a man, who was wise enough in all the common affairs 
of life, stoutly deny the possibility of knowing this distance, because it is im- 
possible that an astronomer should pass from the earth to the sun with a 
measuring rod in his hand. And there are well educated men who have no 
idea whatever, that this distance can be determined otherwise than by a trigo- 
nometrical admeasurement. The value of any distance however, is only large or 
small comparatively ; and compared with the magnitude of the sun, its distance 
from the earth is not great. Let the sun, in the minds eye, be regarded to be 
no larger than a carriage wheel, then, if the distance be proportionally reduced, 
the space between earth and sun would be traversed in about thirty revolution 
only of the wheel. Besides, consider this distance as great or as small in itself, 
the relations of the sun, the earth, and the moon are so intimate and the har- 
mony of their astronomical elements is so perfect and faultless, — one character 
pervading the whole sub-system — that a "little fragment," a comparatively un- 
important part, for instance, the fraction of a period as measured by other pe- 
riods or the fraction or overplus of a distance as measured by another distance, 
will enable an astronomer to reconstruct the system, — to lay off in his mind 
the periods and distances, as these periods and distances were determined by 
Him who placed the Corner Stone of the Earth supporting thereon the heavens ; 
for behold, "all things are double one against another, there is nothing imperfect." 
And man can do this, — not because of the great acumen of his intellect, not be- 
cause of his intense strength of logic, — but because of the simplicity of nature, 
the whole of the works of God being made up of the repetition of perfect and 
analogous parts, one of which being comprehended, leads to the comprehen- 
sion of the great Unity. God has not covered a portion of the heavens only 
with the beauty of harmony. He did not affix a common ratio of the periods 
of the planets to their distances, — controlling this element of the spheres only, — 
and permit accident to interweave itself confusedly over all other elements. 

A good naturalist, from a fragment of one of the bones of an animal, can 


reconstruct its organization, seeing it with the mind's eye as it roamed in the 
forest, as it traversed over the plains, as it was borne upon buoyant wings, or as it 
swam in the waters, before the voice of man was heard on the earth. This 
he can do, because the character of the animal is written out on every part and 
portion of its frame. Thus, also, Newton, from a little fragment of an astrono- 
mical element, to wit — the fall of a body towards the centre of the earth in one 
second of time — mathematically re-created the solar system. This is not the 
only fragment of an astronomical element on which the laws of the universe is 
written out. The position of an isolated ocean rock, the area and contour of 
the terrestrial masses have the character of the heavens stamped upon them. 
And it is not an idle dream that the distance across an ocean may indicate the 
distance of the sun, for there is no part of the creation which is not an integral, 
harmonious part of the whole; no part exists isolated and alone, without 
symmetrical relations with the other parts of the universe. 

Every enquirer for truth should loose his hold on the adopted notions, and/ 
says Sir John Herschel, " should strengthen himself by something of an effort 
and resolve for the unprejudiced admission of any conclusion which shall appear 
to be supported by careful examination and logical argument, even should it 
prove of a nature adverse to notions he may have previously formed for him- 
self or taken up on the credit of others" 

An effort to learn, a struggle for an advance beyond the received doctrines 
is the "euphrasy and rue" by which we must purge our sight before we can re- 
ceive and contemplate, as they are, the lineaments of truth and nature. 

Note to Fourteenth Method, (p. 65), Section 10th. 
The author was advised by a friend to omit the fourteenth method, for finding the mean 
distance of the earth from the sun, on the ground that the method would be deemed altogether 
unsatisfactory; and also, because a reference should never be made in scientific works to the Bi- 
ble. The method is retained, however, for the following reasons: 

It is true that the fundamental, perhaps it should be said, the exclusive purpose or object of 
the Bible, is to teach the will ot God and to open to man the door of salvation. It therefore gives 
the truth in spiritual matters, not truth relating to the material creation, except incidentally. Re- 
member, however, that the Prophets and Patriarchs were the astronomers of their times ; and that 
their thoughts, soaring up towards God, must, necessarily, often have rested on the beauty and 
glory of the celestial spheres, which, immense worlds, in perfect order and faultless symmetry, for- 
ever obey the laws assigned for their positions and motions — their thoughts arrested for a while, just 
as the flight-worn birds, crossing over a wide expanse of ocean, often alight on the masts of a pass- 
ing ship, not as the end of their course or goal of their hopes, but that resting there awhile, they 
may acquire new strength to urge again their flight to reach their nestling place on soma far-off 
island of the sea. 





That there is much Order in the Structure of the Earth's Surface will be admitted: 
is there also a Relation of this terrestrial Order with the Astronomical Elements 
of the Earth; and is there also an Intimate Relation between the rabies of the 
Earth's Astronomical Elements independent of their actual or their supposed 
Physical Causes? 

The reader of this Essay has had his attention directed to three special and 
separate subjects of discussion: In the first place, it has been attempted to 
prove that, capricious and accidental as at first they appear, the terrestrial 
masses, or the various divisions of land and water on the surface of the globe 

In the year 1854, the thought occurred to the author, that, possibly, the septenary division of 
time had its physical foundation on the far prevading law which gives to the periods of the spheres 
one latio to their mean distances from the sun. The result of the calculation as presented in the 
text is. that the six-day planet has a seven sun-diameter distance. 

It is evident, that the septenary division of time is not founded on any open palpable astro- 
nomical period, or on a change of the position of any sphere, readily and generally perceived, such as 
the returning phases of the moon. This follows, because the septenary division is used only from 
China to the Mediterranean sea, among the people of affiliated nations, the ancient histories and 
traditions of which, show a knowledge in ancient times of the science of astronomy far beyond 
that of any other portion of the globe. 

The reasons for a belief in the existence of this high state ofthG science in very ancient times 
will be found in "Vinces' Astronomy." The Rev. Dr. Whewell, by eminence, the Historian of 
Natural Science, says: "there is something remarkable in the prevalence of the notions which have 
produced this result," (the septenary or hebdomadal division of time) " and we may probably con- 
sider, with Laplace, that it is the most ancient monument of astronomical science." To quote from 
a most beautiful article of the North British Review : "when the sevensome analysis of time began, 
history cannot tell, nor inductive science find out ; yet, as the humble disciple of a philosophy older 
than that of Helvetius or that of the Encyclopedias, I have no doubt on the subject — I believe that 
man knew this, and many a far deeper secret, during the prehistoric epoch of human story." 

Ancient Philosophers regarded certain numbers as sacred, and among these, the number seven 
was preeminently sanctified. This has been regarded in modern days, as a "Pythagorean conceit," 
as a foolish notion, denoting the very babyhood of Philosophy. It is a fact, however, that the dry 
husks often remain, after the grain once contained in them, has perished. So the symbols, as the 
envelopes of the truth of the olden philosophy, often descend through generation to generation after 
the truth itself has been lost to the world. The common mind, so far from transmitting the thoughts 
of the truly great, never even fully comprehends them. It must be so, because there is no other 
way of accounting for the reverence of great men for numbers, than on the ground, that certain 
numbers were sanctified or hallowed, because they express'the sacred things of the creation. (Jod 


are law- determined in their forms, extents and relative positions. In the next 
place, there has been pointed out a relation, which, it is averred, exists of the 
figure and surface structure of the earth with its astronomical elements as a 
planet. And lastly, very many calculations have been presented which, in 
their results, show that the values of the astronomical elements of the earth 
are so intimately correlated that the value of either one of them can be readily 
calculated from the values of the others. 

works by plan — by method — by quantities ; certain numbers and certain values are of frequent repe- 
tion in the structure of the universe, and thus these numbers became holy, as they were associated 
with the manifestation of God's Creative Wisdom. Religion itself needs its symbols; it requires 
forms of matter to represent to feeble man its spiritual truths, and to direct him in his upward flight ; 
and, if a symbolized truth is overlooked, this reverence for the symbol appears to the forgetful as 
rank idolatry. Science also has ever represented or materialised its abstract truths in numbers, 
phrases, or in instruments and in diagrams; and when the truths thus represented are forgotten or 
denied, the reverence for its material representations appears ridiculous and childish. 

It is in this aspect only that numbers anciently became hallowed or sanctified. Modern 
physicists, (if this word be permissible,) of pigmy minds as compared with Moses or Plato 
or Pythagoras, would not dream even, of a mystery, sacredness, or of pre-eminence attaching 
to any number by itself, or as one of a, series of numbers, nor would they dream of hallowing the 
sound, letter, character or symbol affixed to any quantity whatever: Why then should they im- 
pute a folly to the truly great of ancient times so palpable as to be detected as folly by those of the 
range of their inferior intellects ?, 

"Ever sin ;e God did set his bow on Mount Ararat, the children of light, with speechful look, 
if not with still small voice, have been saying, seven; and if the tongue is dumb to give it utterance, 
the ear is not deaf to the seven toned rhythm of the universe, nor are the fingers without skill to 
fetch its antitypes out of reeds and pipes and vibrating strings;" and God, by resting on the seventh 
day, He himself, hallowed the number, crowning it with light and glory which has shone, and will 
continue to shine over generation after generation to the end. Deep, indeed, is the mystery of 
creation ; and sacred, indeed, every sign, symbol or value which, thus redeemed from common use, 
stands for, and brings to the human mind a faint conception even, of the awful mystery declared 
by the questions : What are we ? What is the world ? How can we comprehend a God ? 

The christian need not be afraid to believe in a physical basis for the moral law ; he need not 
reluct at the thought of a connection of the dealings of God with the material to the spiritual, as 
the two phases of one law, constituting the union of the results of His sovereign will : and 
when the Sunday bells sound in his ears, calling men together for a common end, sympa- 
thetic worship, and for communion with God, his religious tone will not be weakened, if, to his 
ears, the sonorous peal proclaims also the common bond of the spheres of the solar system, 
and tells of their sympathetic relations to the great luminary, the sun, which, at rest in the 
centre, continually pours forth a flood of light and of warmth and of consequent animal enjoyment 
over its encircling worlds — the one law applies to the moral nature of man, and is exalted because 
fitted for intellectual beings, it is also exalted because this law over the material has been obeyed 
forever by the countless worlds spread out over the infinity of space. 



An inspection of the annexed map of the world, with its many lines show- 
ing the symmetry of the surface-divisions of our globe, will of itself, it is believ- 
ed, convince any man who is open to the reception of new truth, that there is a 
greater degree of order and regularity in the relations of the masses of land 
and areas of water of the globe than has before been demonstrated to exist.* 

The second position here taken, that astronomical laws determine the 
divisions and surface-structure of the earth, it would seem, can hardly be ques- 
tioned ; because, admitting what is clearly before the eye, that there is a law for 
the position of the terrestrial masses, what other law can it be than that which 
acts upon the world as a planet? The immense range of the action of the 
fundamental laws of nature is the glory of creation : 

"This unprofuse magnificence divine 
Is wisdon truly perfect, — thus to call 
From a few causes such a scheme of things, 
Effects so various, beautiful and great, 
A Universe complete! 

The third position of this Essay, that the values of all the astronomical 
elements of the earth are systematically and intimately related, probably, will be 
generally denied, and the results of the calculations previously given in order 
to support this position, will be regarded as mere accidents, as results nothing 
more than "curious numerical coincidences," unworthy of any special attention 
or examination by the received astronomy. This scepticism will arise from 
this : the science of the day recognizes certain physical causes for the earth's 
equations, — for instance, the precession of the equinoxes is attributed to the 
attraction of the sun and moon upon the earth's protuberant equator ; therefore 
the fact that the result, giving its exact value from other values which have 
no relation to, or connection with this value, must necessarily be a hap-hazard 

*The fact that volcanic and earthquake action occurs only on regions which are departures 
from normal extents and contours as clearly shown in this Essay, proves the main position of law de- 
termined order — the exceptions proving the law by the exhibition of phenomena from which the 
other portions of the world are exempt. The elaborate report of Mr. Mallet, (1858) who has devo- 
ted many years ofhislifeto the investigation of earthquake-agency, shows the position of volcanic 
action very much as presented theoretically in this essay. Mr. Malet's map places volcanoes, &c, 
on broken and abnormal coasts. To quote: The normal type of superficial distribution of earth- 
quake action, "is that of bands;" •'these bands very generally follow the lines of elevation which 
mark and divide the great oceanic, or terr-oceanic basins (saucers) of the earth's surface ; earthquake 
agency is "greater and more frequent as the great lines of volcanic activity are approached." 



This argument has the appearance of soundness, but it will not bear the 
test of a close scrutiny. Let it be admitted that the assigned physical cause of 
the precession is the true and veritable cause, nevertheless, the value of this 
equation, on sound principles, may be calculated from the value of other 
equations which have their own special physical causes. God, for an ulterior 
result, may have so proportioned the attracting power of the sun and of the moon 
and of the equatorial regions of the earth that the value of the precession may 
be calculated from the value of the obliquity of the ecliptic. The ulterior re- 
sult being a harmonious relation of the associated phenomena; therefore, the 
one is calculable from the other by him who understands the harmonious rela- 
tions. The argument against the position of this Essay founds itself on the un- 
phjlosophical idea, that masses are accidentally determined without ulterior 
plan. A steam engine, as an active agent or motor, will elevate a certain quan- 
tity of water in a certain time to a certain height according to its power; it is not 
improbable however, that the mechanic constructing it may have proportioned 
its duty or capacity of work, so that the quantity of water raised may be in a 
due and fixed relation to the other requirements of the special mechanical pro- 
cess for which the engine is used. The error consists in considering that the 
means of God's action, his reservoir of force, is not controlled to produce results, 
beyond and beside the action which is discovered and incorporated into the 
system of astronomy, If results or relations other than those accounted for are 
proved to exist, there is no danger in supposing that the forces of nature are 
controlled and arranged so as to produce them. There are, let it be supposed, 
two vessels built to sail on the ocean; both are constructed by the same means, 
materials, and processes, and are held together by the same laws of gravity, co- 
hesion, friction, and the like. These vessels, however, differ essentially in 
magnitude, in model, and in the general relation of their parts. In like man- 
ner, another solar system may be supposed to exist, and being produced and 
maintained by gravitation and other received laws, still notwithstanding this, 
the one system may essentially differ from the other in the number, position, 
and magnitude of its spheres, in the inclination of their axes, in the form and 
obliquity of their orbits, in the velocities of axial rotation, in the direction of 
their orbital and axial motions. The law of gravitation may be regarded as only 
an instrument by which the solar system is built up and maintained. Now, 
the results of the action of gravitation depend on the assigned masses of the 
spheres and their assigned position. These masses and these positions are so 
determined that certain harmonious results are produced. The received astron- 
omy confines its attention mainly to the action of gravitation, while the pre- 


sented system regards the result of the harmony produced by mass and posi- 
tion. There need be, therefore, no opposition to the presented facts of sym- 
metry from the most conservative votary of the received science of astronomy. 

And let here, a serious and pertinent question be asked of conservative as- 
tronomers: If, in some fifty instances, by simple and analogous processes, cer- 
tain astronomical elements are reached in their values by use of the values of 
other elements — these resulting values and the values as data of the calcula- 
tions being those from observation, what is the probability, on the doctrine 
of chances, that the results are only fortuitons numerical coincidences? If the 
answer be, that it is very improbable, so much so as amounts almost to a certainty 
that the results are not accidental; are they, then, as custodians of learning ; 
in the discharge of the duty they owe to truth in setting aside the presented 
results of this Essay as mere numerical coincidences unworthy of attention ?* 

The great obstacle, however, to the reception of the last position as truth 
is that the results have been presented as existing facts only, without a system 
for their union and without a great truth, or general rationale or idea or first 
principle as a basis or reason for their existence; this is now to be supplied: 

There are two fundamental laws which pervade the whole structure of the 
universe, and which act on every part of the body of nature from its great trunk 
to each limb and minute appendage. The first of these laws is Affinity of Struc- 
ture. There is a normal form or type which, in the various entities or indivi- 
dual existences is changed or abated, and never altogether departed from, the 
changes being only to the extent made necessary by the varying positions and 
functions ot the different individuals. 

The second of these laws is, the Composition of all Entities or Forms by an 
aggregation of sub-entities or sub-individuals — the sub-individual retaining 
as much an independent existence as possible, in view of its position and func- 
tion. In place of using a further verbal description or explanation of these laws 
instances of their results will better convey the idea. 

By affinity of structure, all the worlds of the solar system are spheroidal 
in form ; they all have inclined axes of rotation ; they all move in oblique and 
eccentric orbits ; their distances have one common ratio to their periods, and so 

*It should be mentioned, that it is very possible, nay, very probable, that some of the present- 
ed calculations are erroneous in result ; but, the number which will be found correct is sufficient on 
which to base the question asked in the text. It should also be remarked, that the calculations are 
not in many cases extended to extreme fractional nicety, round numbers being used at times when 
a greater nicety is not required to exhibit the principle under discussion. 


on. And again, the solar system is a part or division of the great Astral Uni- 
verse, and the solar system itself, is sub-divided into groups of worlds, (of Avhich 
the family of planetoids is a marked instance) . There are also sub-systems of 
spheres, composed of a planet and satellite or satellites. Then come the sepa- 
rate worlds, each world existing as an individual entity. 

The presented system of united geography, geology, and astronomy, is 
founded on these fundamental laws of the dealings of God with his material crea- 
tions. And this system differs from the received system only in this : the appli- 
cation of the law of affinity of form, division of entities, and the general corre- 
lation of the parts of the solar system is further extended and more intimately 
and thoroughly applied. For instances of this : the earth's axis of rotation is 
inclined relatively to the plane of its revolution,* and so, in conformity, is the 
position of the sun's axis thus inclined; it is averred that these two facts or 
forms are identically of the same nature and normally would be of one value. 
But, the degrees of the inclination of the axes of the two spheres differ in value. 
This difference flows, then, from a special position of the earth, — from the spe- 
cial magnitude of the earth, and from the velocity of the earth's axial rotation, 
all differing in value from those elements of the sun. Thus, the value of the 
inclination differs, and this value is calculable because of, and from the vary- 
ing circumstances attending the two spheres. In section Eight, the mean incli- 
nation of the Earth's axis is calculated on these principles; and the result then 
obtained, is proved to be correct by the fact, that as the number of the sun- 
diameters, contained in the earth's mean distance from the sun, is to the number 
of the days of the earth's year, (which is determined in value by the axial ve- 
locity and magnitude of the earth), so is the value of the sun's inclination of 
axis to that of the earth's mean inclination of axis, (24° 26'). This appears 
simple, for were the earth's distance of the sun nil, and had the earth no 
special axial rotation, it would have its degree of axial inclination as the sun's. 
Or, to express the position more clearly: it is the special circumstances atten- 
dant on the earth as an individual sphere which makes its axial inclination 
differ from that of the sun's. There is by nature an adherence to form which 
therefore is changed only because of special position or function of the indivi- 

* This is usually called " the obliquity of the ecliptic." The expression appears to be of ques- 
tionable propriety, as it makes the plane of the earth's revolution of an orbit 24,000 larger, than 
that of the orbit of the plane of the axial rotation, oblique to this far lesser plane of motion. The 
phrase is a heir-loom descending from the times when the earth was considered motionless, and the 
ecliptic, as denoted by the stars, was deemed to be in motion. 


dual entity; and to the degree of the change of position and function, the change 
or variation from the normal form is restricted. This reason extended, forms 
the rationale, generally, of the harmonious relations developed in this Essay. 

The minor astronomical element, — the equatorial protuberance of the 
earth, — as has been determined by structural affinity, and as given by geodetic 
measurement, is 3-^.T of the earth's diameter, or 26,227 miles. This, the equa- 
torial excess, or, in more expressive phrase the ellipticity of the earth's figure, 
is the most prominent of the astronomical divisions of the earth. It has spe- 
cial distinctive characteristics; it is, more highly than any other division, the 
subject of independent action of the planetary laws which govern the earth as a 
sphere. Nature does not proceed per saltum; she advances in close and almost 
undistinguishable gradation; and hence, the ellipticity of the earth's figure 
is a connecting link between the whole world as a planet and the sub-individ- 
ualities of the terrestrial surface-masses. It is to be regarded as an embryo 
satellite or rather as a nascent ring of the type and character of the rings which 
surround the planet Saturn. To prove this position, and to show most clearly 
that the earth's planetary laws act on this portion of the globe, with a degree 
of independent action, the following discussion is presented. 

There is a structural affinity between the ellipticity of the earth's figure and 
the ellipticity of its orbit. The ellipticity of the orbit, as shown by the motion 
of its apogee and perigee or the points of orbit which are the nearest and furthest 
position of the earth relatively by the sun," revolves, (see section Seventh), 
completing a revolution around the orbit in 110,340 years. Now, the follow- 
ing fact is most conclusive as to the soundness of the principle under discus- 
sion. The product of the value of the ellipticity of the earth's figure multiplied 
by the number of the years of the period of the sun's perigee is equal to the pro- 
duct of the earth's diameter multiplied by the number of days of the year. 

The ellipticity of the earth's figure is in diameter, 26,227 miles; add -^\^ 
(the ratio of this ellipticity to the diameter of the earth) and the sum is 
26,332; the diameter of the earth is 7,926 miles; add as in the former case 
_l_ of it (= 26) and the sun is 7,952 miles, thus: 26.33 x 110,340 = 2,904,572, 
and also 7,952 x 365.24 = 2,904,572, then the product of one equals the product 
of the other. In this common measure, 2,904,572 miles, there is once the earth's 
diameter for every day of the year, and also once the ellipticity of the earth's 
figure for every year of the periods of the revolution of the sun's perigee or ellip- 
ticity of the earth's orbit. 

The advantage of the presented method of investigation appears in this: 
to reach one fact of harmonious relation is vantage ground from which other 


facts of this character are discoverable: Thus, the value, 2,904,521, less T J T of 
it, or 170,855 is the value of the sun's circumference, the sun having a diameter 
of 870,167 miles, (see section Ninth); in another form of expression, the sun's 
circumference, plus 1 1 ¥ of it, equals 110,340 times the ellipticity of the earth's 
figure, and also 365.24 times earth's diameter, as before stated : — The sun's 
diameter, 2,733,672 + 170,855 = 2,904,527 miles, the common measure. 

This ratio T ' T thus unfolded is indeed an index to other harmonious rela- 
tions; it is, in fact, a key to unlock many of the mysteries of the solar system. 
Thus, the mean inclination of the earth's axis from the perpendicular, or as 
usually expressed, the mean obliquity of the ecliptic, is 24° 26' and its secular 
oscillation from this mean is 1° 31' 43" ; these values, not known with any 
reliable exactness by the received astronomical system, were calculated on the 
system of Structural Affinity, and the values were proved to be correct bv a 
subsequent conrparison of them with certain other elements, (section Ninth). 
Now, the accuracy of the values, as before assigned, is thus demonstrated: 
1° 31' 43" to 24° 26' is as 1 to 16; and from this ratio T ' T , and from the value 
of the sun's circumference, the values of the diameter of the earth and of the 
ellipticity of its figure are correctly calculable. 

To obtain a common measure of the diameter of the earth as a whole, and of 
the ellipticity of the earth's figure as a part of the earth, which is individually 
obedient, in some degree, to the laws of the whole earth, T ! T of its value, is 
added to the circumference of the sun. Let the fact be stated in another light: 
In place of increasing the circumference of the sun, which would increase the 
period of rotation with the same axial velocity, let the velocity be reduced in 
the same ratio, prolonging the period of rotation to the equivalent degree. The 
number of the days of the actual period is 25.212; 29.212 plus T ' T of it == 26.787. 
This, plus i-o y . T of it = 26.80 — clays. The sun's velocity of axial rotation is 
4.34 times that of the earths: 4.34 as diameter gives 13.64 as circumference; 
then, 13.64 x 26.80 — = 365.24, which is the number of days of the year. 

The ratio of the sun's period of axial rotation to the period of the earth's 
year, expressed as 25.212 to 365.24, throws no light whatever on the relation of 
the two elements. On the other hand, the relation begins to take a definite 
form when the ratio is thus expressed: the period of the earth's revolution in 
days equals the period of the sun's rotation in days, plus T 'g-, plus -s^ T . T multi- 
plied by the difference of axial velocity and multiplied by the ratio of the 
diameter to the circumference of a circle. 

This result is on the assumption that the sun's equatorial velocity is 4.34 
times that of the earth's. Let this be proved to be the true ratio on the system 


of Structural Affinity : the diameter of the earth's orbit is 190,750,000 (section 
Tenth) ; the sun's circumference is 2,733, 672 miles, which values are to each 
other as 1 to 69.777. Then 69.777 divided by the ratio, sixteen, gives 4.34 as 
the ratio of the two axial velocities (the earth's and sun's) to each other. This 
path of investigation is opened only, it is not in the scope or object of this Essay 
to proceed further in the opened path. 

The mean distance of the earth from the sun is one half of the diameter as 
used in the preceding paragraph as one of the data in the calculation. Is it 
asked how, on the system of Structural Affinity, this value of the diameter of 
the earth's orbit, 190,750,000, and the resulting mean distance, 95,375,000, 
miles, can be proved to be correct? 

The data required are: the ratio, 16; the days of the year, 365.24; the 
number of the sun's rotations in one year, 14.5; the moon's mean distance 
from the earth, 237,319 miles. The process is short and very significant: 
365.24x16=5,844; 5.844-14.5=403.20; deduct for the ellipticity of the 
oarth's figure ^2- (=1.33) and the remainder is 401.87; then, 401.87 times 
237,319 equals 95,375,000 miles, which is the required element of the mean dis- 
tance of the earth from the sun. This, as the value of "the fundamental ele- 
ment of the solar system" is a value common to all the results of the presented 
processes, amounting to nearly fifty in number. Therefore all the values used 
in producing the common result in the preceding calculation are the true 

To return to a former statement: the period of the sun's axial rotation,, 
25.212 plus -jig = 26.80 days, or the equivalent of a rotation of a circumference 
16 times larger than the actual circumference of. the sun with its actual axial 
velocity. The sun's circumference is contained in the earth's orbit 219.24 times. 
Now, if the sun rolled through the earth's orbit with a period of axial rotation 
of 26.80— days, it would require (26.80x21924=) 5,875 days to complete 
the orbit, — this is 16 years and 31 da} r s; and how to account for the overplus, 
of 31 days, the author admits that he knows not, 

To calculate the ratio of the earth's orbital to its axial equatorial velocity 
is a very simple process: The sun's circumference plus T ' T as before equals 
2,904,527, and the diameter of the earth's orbit is 190,750,000 miles; 2,904,527 
is to 190,750,000 miles as 1 to 65.8— the required ratio (65.77) ; Thus, 
it is not the value of the sun's circumference in its ratio to the amplitude 
of the earth's orbit alone, but it is the sun's circumference increased by the 
ratio of the secular oscillation of the obliquity of the ecliptic to its mean 
which determines the important ratio 1 to 65.8. This ratio 16, the sun's 


sun's circumference, and the amplitude of the earth's orbit are jointly the source 
of the ratio under discussion. If this important ratio of the earth's orbital to 
its axial velocity flows from, and is dependant upon, or is, in any manner or to 
any degree in correlation with the value of the earth's ellipticity of figure, then, 
most surely, this ellipticity has not its individuality altogether merged in the 
individuality of the earth as a planet. And the fact that the value of the earth's 
ellipticity of figure, of, and by itself, to some degree, is in affinity with astro- 
nomical elements, will not be doubted, resting the faith alone on the fact now 
presented, and on the fact that there is once the value of the earth's excess of 
equatorial diameter for every year of the period of the revolution of the sun's 
perigee, while there is once the value of the earth's diameter for every clay of 
the period of the annual revolution of the earth in its orbit around the sun. 
But these two facts are not the only foundation for the belief. 

The subdivisions of the Earth in their relations to its astronomical elements 
are now the special subject of discussion. As preliminary, the attention of the 
reader is aeain directed to the following facts of harmonious correlation : 109.6 
times the sun's diameter equals the mean distance of the sun from the earth ; 
109.6 times the earth's diameter equals the diameter of the sun ; and 109.6 
times the moon's diameter equals the mean distance of the moon from the 
earth. It will be perceived, that diameter measures distance by the same 
ratio ; therefore there is a harmonious relation between diameter and distance 
in certain cases at least, that is, distance and diameter in these cases are anal- 
agous or under the same law, because, in the threefold repetition of this ratio 
a diameter in one instance is substituted for a distance. 

The received system of astronomy recognises, it is true, a relation between 
the distances and the periods of the spheres. The system, however, goes no 
further than this ; it does not teach that the distances of the spheres from the 
sun, or from each other, are law-determined. This element of the solar system, 
relative distance, is not attached to, nor is it placed in correlation with, any 
other astronomical element whatever. 

It is acknowledged, that the diameter of the sun is to its distance from the 
earth as the diameter of the moon is to its distance from the earth, and also as 
the diameter of the earth is to the diameter of the sun, for the facts are derived 
from the measurement of these diameters and distances. But, from a charac- 
teristic fault of many scientific men, it attributes to chance-happenings, or, in 


the usual phrase, to " a curious numerical coincidence" all such facts, for which 
no place is found under the received theories. A sound philosophy, however, 
frowns at the idea that any chance-work is to he found in the works of God, 
and requires that these men should admit that there is a law for such result.-, 
although the admission is a confession of their own ignorance. 

In all architectural structures, in order to preserve the harmony of the 
parts, a " module" or common measure is selected ; this, hy itself, or in its 
sub-divisions or in its multiples, is every where repeated; it is not only the 
measure of the parts of the structure, but it is also the measure of the distances 
of these parts from each other ; thus, for instance, it determines not only the 
magnitude of the columns, but also the degrees of space between them ; 
otherwise incongruity and disproportion would offend the eye. It is so in Ma- 
ture. A tree, for instance, is symmetrical, not only because the sizes of the 
limbs and branches are in certain proportion to the diameter and height of the 
trunk, but also, because the limbs and branches are correspondingly determin- 
ed, so that their distances from each other,, combined with the magnitude of the 
parts give harmony and symmetry of form. In like manner, the solar system 
is a perfect whole, the symmetry of which arises, not from the magnitude and 
the number of its worlds alone, but also from the relative positions in space 
which these worlds occupy in the heavens. In fact, philosophically and truly, 
distance and magnitude have no line of separation whatever; they are of the 
same nature; a measure of the magnitude of the most solid body involves the 
measure of the spaces by which the atoms constituting the mass are separated 
from each other. 

Besides, the space between the earth and the sun, is as much a constituent 
part of the solar Edifice of Worlds as the magnitudes of the sun and earth ; 
because, it is the value of this space or distance which determines the orbital 
velocity of the earth; and, as has been clearly shown, the velocity of the earth 
in its orbit is in correlation with the velocity of the sun's axial rotation. 

The threefold application of one ratio to the distances and diameters of the 
sun, the earth, and the moon, stands not solitary and alone among the visible 
manifestations of harmony of this character; there is a fivefold application of 
another ratio (402.23) to the astronomical elements of the three spheres, (me- 
thod 25, page 73) . Further, these are not only valuable additions to our knowl- 
edge of the spheres, but they are indices to other discoveries, the ratios pre- 
sented being as outcropping surface-ore which indicates a mine of cxhaustless 
mineral, the working of which will add greatly to the wealth now in the 
treasury-house of the science of astronomy. 


On the existence of a God who loves and preserves faultless symmetry 
throughout this creation, or in a more subdued expression, on the action of the 
law of Structural Affinity through the subdivisions of the solar system, it fol- 
lows that neither the threefold nor the fivefold repetition of one ratio are from 
mere accident, or are lawless results. Therefore, if this be the case, the harmo- 
ny ends not here ; and the search for the value of the moon's diameter as deriv- 
ed from its relations to other elements is hopefully made ; and the result, if 
successful, will give the positive distance of the moon in miles by multiplying 
the discovered value of its diameter by the number of times it has been found 
to be contained in its distance. Nor will this practical result be the only value 
of the discovery, because, it will show that the direction of the search is sound, 
and this direction was indicated by assuming as a fact, that there is a law for 
the threefold application of the ratio which has been under discussion. For it 
will not be denied, that if the search for the value of the moon's diameter is 
successful, because of the soundness of the principles on which it was commenc- 
ed, the success completely overthrows the supposition that the threefold ap- 
plication of the ratio of 109.62 is naught but an accidental propinquity or ar- 
rangement of arithmetical digits. 

It has been shown, that the value of the sun's circumference enlarged by 
one sixteenth equals 365.24 times the earth's diameter, and also 110,340 times 
the excess of the earth's equatorial over its polar diameter, — 365.24 being the 
number of the days of the earth's annual revolution; and 110,340 being the 
number of the years of the revolution of the sun's perigee. The value added 
to the sun's circumference being t l of this circumference; therefore j ] T of the 
sum or value obtained is equal to T \ of the the sun's circumference ; T ' T of the 
value of the sun's circumference plus T ' T of it, is 170,850 ; T ' T of which is 10,080; 
add -3-j 2.T (f° r which see page 13) = 33,and there is 10,083 miles, which is 
the sum of the earth's and the moon's diameter; deduct 7,923, which is the 
value of the earth's mean diameter, and the remainder 2,160 miles is the value 
of the moon's diameter. If this result was only very approximately the true 
value by observation, it would be sufficient to prove the position taken ; but 
the result obtained is correct with minute exactness. The diameter of the moon, 
so near to the earth, is measurable with great nicety, and measurement gives 
2,158, or as usually taken, 2,160 miles. 

The process is demonstrated to be sound not only by its result, but because 
it was indicated by principle. The value of the sun's circumference plus T ' T , 
with the number of the days of the year as coefficient, gives the value of the 
earth's diameter, and the same, with the number of years of the period of the 


sun's perfgee as coefficient, gives the value of the ellipticity of the earth's figure; 
there is a manifest correlation between the earth and moon ; therefore, from the 
same value, the diameter of the moon can be calculated as it has been done. 
Besides, a correlation between the moon and sun is indicated by the fact, that 
the moon's distance from the earth in repetition of its diameter is equal to the 
distance of the sun in repetition of its diameter. 

To repeat the idea: As the diameters af the sun and moon are repeated 
an equal number of times in their respective distances from the earth ; and, as 
distance is as fully an element of the structural harmony of the sub-system of 
sun, earth, and moon, therefore the diameters of sun and moon are correlated 
in value. This- is also shown by a fact before presented, that the distance of 
the moon from the earth in its mean, which was determined by its diameter, is 
T -^2- of the moon's mean distance from the sun, and that the moon's diameter 
is T |-3 of the sun's diameter. 

From all these considerations, not a suspicion even can rise in the mind 
that, for instance, the distance of the moon from the earth was not determined 
in relation to its diameter by a general law establishing other relations of this 

Among the often repeated ratios, that of 109.6 applies, first, to the rela- 
tion of the sun's magnitude to its distance from the earth; and, in the second 
place, to the relation of the diameter of the earth to that of the sun, and, third- 
ly, to the diameter of the moon relatively to its distance from the earth. The 
application of this ratio ends not here. It is not limited to its application to the 
earth's actual satellite, the moon. It reaches lower than this. It also applies 
to the earth's ellipticity of form, which is a sub-entity of the earth, and which, to 
a degree, exists independently as an enbryo satellite or nascent ring which forms 
the connecting link of the great chain of subdivisions extending from the sun, to 
embrace and to fold into unity the subdivisions of the earth. For, accord- 
ing to the positions before taken, the terrestrial masses of the earth are 
individual entities, and to a degree the subject of the independent action of the 
laws of the spheres ; and the redundancy of the earth's equatorial regions is one 
of these individual entities which, as a step upward, extends the relation, first 
to the moon, and thence to the sun, which as an independent sphere, is fully and 
altogether under the control of astral law. 

The fact that the law of the relation of the diameter of the moon to its dis- 
tance from the earth extends to the surface divisions of our globe, will appear 
at first to many, as of very doubtful soundness ; staid science is seen to shake 
its head in dissent, — even a slight deriding curl of the lip is visible, changing 



somewhat its usual composure of expression. But, nevertheless, "the world 
does turn on its axis," and the sun, motionless at the centre of the earth's revo- 
lution throws not only light and heat over its family of worlds, but also, from 
this Central Luminary flows outward the beauty of symmetry with which all 
its attendant spheres, and all the subdivisions of these spheres, are clad. 

For the proof: The excess of the earth's equatorial, over its polar diameter,. 
is 26.227, which adds to the equatorial circumference 82.47 miles. The distance 
of the moon is 109.6 of its diameters; 109.6 times 82.47 equals 9.020 miles. Let 
now (see page 73) T ' T , or 564 be added thereto, and there is before us the value 
of 9,584 miles. It will be remembered that the sun's circumference plus T \ 
equals 110,340 (years of the revolution of the sun's perigee) times 26.227 (the 
excess of the earth's equatorial diameter). There is now for examination, 109.6 
times the excess of the equatorial circumference of the earth plus y \; and this 
is found to be 365.25 (days of the year) times 26.227 : (365-24 x 26.227 = 9,584; 
9,584— T ' T = 9,020; 9,020-109.6 = 82.47; 82.47 ■*- 314159 = 26.227). It 
cannot therefore be denied, that astronomical elements, as data gives to us 
for discussion a subdivision of the earth of 9,579 miles, equal to 138° arc of a 
great circle of the earth, 69.2 X miles being the value of one degree. 

The position of the earth's magnetic, is oblique to its geographic, equator 
at an angle of 19° 47' ; the fact is now presented as derived from observation. 
Let there be stretched across the equator at the angle of 19° 47', the arc of 
138°, the value of which has been astronomically determined. How far will this 
arc extend ? What prominent earth-division will its termini touch and indi- 
cate? In reply: this arc extends from Tropic to Tropic. Thus the arc 138° 
is a measure of a fundamental astronomical division of the earth's surface-* 
it being the range of the sun's annual declination. 

Still further : Take the distance of the tropics from observation ; stretch 
a line across the equator at 19° 47' angle, and mark the points where this 
line touches the tropics. It will be found that these points of contact are dis- 
tant 130° arc or difference of longitude. What, then, is the distance of the 
moon from the earth, as calculable from these terrestrial data ; 130° arc = 9,020 
miles (of a great circle) ; the excess of the earth's equatorial circumference is 
82.47 ; 9,020 -*- 82.47 = 109.6, the answer. Hence, by the law of Structural 
Affinity there is obtained from these earth divisions the thrice repeated astro- 
nomical ratio of 109.6, which is, first, a measure of the relative distance of the 
sun ; then, of the relative diameter of the sun ; then, of the relative distance 
of the moon ; and lastly, the value of an astronomical division of the earth, 
which is founded both t on the distance of the tropics and on the position of 


the earth's magnetic equator. Has it not been proved, that the law which 
determines the relative distances of the spheres as entities, also extends and 
governs the values of the sub-entities of the earth's surface divisions ? 

Here let the fact be recalled that, either with the ratio, or without the ratio 
T ' T (as just used, and as used in page 84), the magnetic equator can be theoreti- 
cally located; and that this astronomical location of it has never before" been 
made, — the knowledge of its position having been empirically derived from ac- 
tual observation. Let it also be recalled that on the most sound first princi- 
ples, those of the extension of Structural Affinity, and of the extension of the 
Subdivision of individual Entities, a very important fact has been reached. 
When the principles are unassailable and when their results are those given by 
actual observation, it would mark weakness not strength of intellect to ignore the 
process. Let it also be remembered, that Meteorology languishes for lack of sys- 
tem to bind the results of its observation into unity, and that this science has 
its dark places continually before our eyes, lighted not by a solitary ray from 
any other branch of science; then surely, it may] be hoped, that in the con- 
joined action of astronomy and meteorology, the former may aid its weaker 
brother, and teach how, and by what law, the magnetic equator and its deriva- 
tive meteorological curves have been determined. 

Although somewhat out of place in this connection : as the distance of the 
moon, &c, has been calculated by the values of the earth's divisions, for data, to 
be 109.6 of its (the moon's) diameters, and as, by the same process the distance 
of the tropics has been determined; then, from this distance of the tropics as 
obtained from measurement, the distance of the sun from the earth can be calcu- 
lated in miles. The distance between the tropics, 46° 56' arc of a great circle, 
is 3.219 miles ; add T ' T (page 84) and the sum is 3.420; 3,420 -*- 3.1415 = 1,086 
miles is a value to be thus used : 

The fraction of a day in one tropical year is 0.24224 of a day and Tl -£ ST of 
a year. This fraction of the earth's orbit is (y^'ot "*" 365.24) TTT ' TTT of the orbit 
for every day of the year. To eliminate the fraction and to end the year in 365 
days the earth must move through -yy-.TrT °f ^s orbit more than it now moves 
every clay. There was, above attained, from the distance of the tropics, a value 
of 1086 miles; thisis TTT ; TTT of the earth's orbit; 551,147x1,086=599,500,000, 
as the orbit of the earth, the radius of which is 95,375,000 miles. Here is 
another of those results which now must be called, interesting relations of the 
heavens and the earth and no longer " numerical accidents." 

The result of the foregoing, to wit, the mean distance oftheearth from the 
sun, is correct. The element has been calculated from the value of a sub-di- 


vision of the earth, with the aid of the fraction. On the correctness of this 
result alone the principle of the application of planetary laws to sub-divisions of 
the earth could be safely rested. But this is a small part only of the evidence 
which is to be presented for consideration. 

There is not the most minute astronomical value which is not determined 
by law. When the earth has ended its year, or revolution around the sun, 
it has not ended an axial rotation, but it has turned on its axis 365 times and 
0.242 arc of its circumference, as a fraction of a day or rotation. If the earth's 
velocity in its orbit were greater daily by -s TT ] TTT °f ^ s orbit, the year would be 
shorter, and end at the completion of an axial rotation or a day. This increase 
of orbital velocity, thus to eliminate the fraction of a day in a year, is 1,086 miles 
for every day; one half of which is 543; the sun's distance is 109.6 of its 
diameters ; add to 543, -rl-g-.-g- of it, and the sum is 547 ; seventeen times of which is 
9,300 miles. This is the mean of 138° arc = 9,579, and 130° arc = 9,420 ; and 
9,579 is T ' T greater than 9,020 miles. Thus, the governing measures of the 
earth's sub-divisions, 138° and 130° arcs, are verified by being calculated from 
the value of a fraction of a day in a tropical year; this being the converse of 
the process by which, from the same values as data, the distance of the sun 
from the earth was before calculated. 

To show that the fraction of a day is not only a part of the system relative- 
ly to the sun's distance, but also to the dividing arcs of the earth's surface, the 
value of this fraction of a day in one tropical year will be calculated, by the 
aid of the ratio 16, from the ratio of the earth's equatorial axial, to its orbital 
velocity, to wit, 65.8: thus, 65.8 -*■ 16 = 4.11 + ; and unity or one day, -^-4.11 + 
= 0.24224, which is the fraction, the value of which is sought. * 

The value of 543, as derived from an earth measurement, was increased 
in a preceding paragraph by T7 V.t °f ^, making 547 miles. From this, 547, 
deduct -gi- (which is one half of the ratio of T ' T ) ; and there remains 530; 
in the first place, 547 x 3.14159 2 , — the square of the ratio of the circumference 
to the diameter of a circle, — plus jjj . T and the product is, say, 5455, which is 
the annual velocity of the sun's perigee ; this, multiplied by the years of the 
period, 110,340, gives the value of the earth's orbit. Besides, 530 times 5,455, 

* The fraction of a day in a tropical, which is the natural year or period in which the sun, leav- 
ing say the north tropic returns again to it, is 0.2422. The fraction of a day in a sidereal 
year or year by the stars, which is the tropical year plus the annual precession of the stars, is 
0.256. These values, 0.242 and 0.256 differ J_ (the common ratio) less _ i__ (the excess of the 
earth's equatorial diameter). Thus, the ratios _i_ and i_. T > £ ive tl,e value of tlie P reces " 
sion, &c, which constitutes the difference of these fractions. 


the annual velocity of the sun's perigee, is equal to the value of the sun's cir- 
cumference plus J T of it, and also equal to 365.24 times the earth's diameter 
and so on. 

The sun's circumference plus -J-g- of it, = 2,904,700 ; the earth's diameter, 
7 937 r»lim '- — 8 433- - ] - = ^.3_° • -5-3-0 r>lus -J- - 3455 miles 

I ,OOI pi US y-g- (D^OfJ . )6 2,904,700) 2,904,7110 1""* 302.1! 5 uwu ""ACSS, 

which is the annual velocity of the sun's perigee or TT J Tr? of the earth's orbit. 
There appoars to be no end to the links of this chain of harmonies. 

The distance of the earth from the sun is thus written out, in bold charac- 
ters upon every astronomical element, — on the tiny fragment of a day in a year, 
on the surface of the sun itself; it is to be read from the protuberance of the 
earth's equator on which the foot of man is placed, and from the motion of the 
sun's perigee which requires for the completion of its revolution more than one 
hundred thousand years. And from the sun's distance the value of the earth's 
surface-divisions can be mapped out, because perfect harmony crowns the works 
of God, from His majestic spheres down to the component parts of the smallest 

This discussion is apparently out of place in this connection. It has been 
here introduced for three reasons : first, to show the prevalence of the ratio of 
16 which is, afterwards, to be fully explained; to show the relation of astral to 
telluric elements ; and, mainly, to prove that the arc of 138° which, in difference 
of longtitude, is a measure of the earth's surface- divisions and a dividing line 
of the terrestrial masses, is of planetary origin, being determined in value by 
the law which has affixed the magnitudes and the distances of the spheres of 
the solar system. 

The first application of the measure of 138° arc will be understood by the 

diagram at the southeast corner of the map. This arc ( ) runs 

from tropic to tropic, and the arc, continued as a circle around the earth, 
passes 180°, or one half of it, over land broken only by a narrow and shallow 
part of the Atlantic ; and 180°, the other half of it, over ocean-waters, altoge- 
ther unbroken by land. This equal division of land and water under this 
section of 19° 47' angle, oblique to the equator, shows a symmetrical construc- 
tion of the earth's surface ; and that there is naught accidental in the rTosition 
of the terrestrial masses, the breadths of land and the extents of ocean water 
being determined by the action of one law which raises and which also de- 
presses the surface of the earth ; and that these mutations are under the same 
law by which the level of the earth's position in its orbit changes relatively to 
the sun, for, at apogee, the earth has risen up from, and at perigee, it has fallen 
towards, the central luminary, exactly as in a longer period, the level of portions 


of the earth's surface changes, by elevation and depression, in distance 
from the axis of the diurnal rotation of our globe. 

The arc 138°, which, continued to a circle, divides the earth into equal 
divisions of land and water, is also the measure in latitude, and also in longi- 
tude, of the major axes of the continents. See on the map the lines 

of 138° arc stretching exactly across Europe- Africa, and also across the northern 
regions of the Western Continent. This is also the measure of ocean-breadths : 
for an instance of which, examine this line which passes from Africa to Austra- 
lia across the Indian ocean, and so on. 

From this measure of 138° arc the other lines of measurement on the 
earth's surface are derived. Those of 84° arc, the minor axes of the continents, 
thus indicated , and the semi-minor axes of 42° arc, thus ex- 
pressed , are derived from the arc 138° by two methods. 

The first method of calculating the arcs 84° and 42°: there are instances 
in which 138° arc measures the extent over a continent and continuously on the 
same parallel of latitude, over an ocean ; 138° x 2 = 276° ; there is then left 
(360° — 276° = ) 84° arc, which is the minor axis of the continents, and, of 
course, one half, or 42° arc, is the semi-minor axis of the continents. 

To the second method, the attention of a reader desirous of finding the 
truth on this subject is to be^directed in an especial manner. It was shown 
at the close of the last section, that so deep and intimate are the relations of 
all the parts of the universe, and so completely faultless is the symmetry 
between the divisions of the earth's surface and the far off comparatively, 
majestic, and immense elements of this system of worlds, that, even, the dis- 
tance of the sun can be calculated from the surface-divisions of the earth. 
This now is to be shown, not to be mere rhetoric, nor a fanciful, wild dream 
of an enthusiast who has fallen asleep while pondering on the subject of the 
harmony of the spheres. 

If the sun has the distance assigned, (see section Tenth), the ratio of the 
number of the sun-diameters contained in its mean distance to the number of 
the days of the year is 3.332 ; and it also follows from this distance, that the 
ratio of the earth's orbital to its axial equatorial velocity is 65.8 ; and, also, 
that the diameter of the earth's orbit contains 69.8 -t- times the sun's circumfer- 
ence. These are the astronomical data to be used. The data arising from the 
value of the earth's sub-divisions are, 138° arc, containing 365. 24 times the excess 
of the earth's equatorial diameter ; and 130° arc, containing 109.6 times the 
excess of the earth's equatorial circumference ; another element used, is the ratio 
of the circumference to the diameter of a circle, to wit, 3,14159. 


Let 130° arc, which is 109.6 times the excess of the earth's circumfe- 
rence, be divided by 65.8 +, which is the ratio of the orbital to the axial 
velocity of the earth, and the quotient is 1.97° + . Let 138° arc, which is 365 
times the excess of the earth's diameter, be divided by 69.8+, which is the 
number of times the sun's circumference is contained in the diameter of its orbit 
around the sun, and also, again, the quotient is 1.97° +. Is it credible, let it be 
asked, that the equality of these quotients is naught but an accident? 

This, however, is far from the full proof. 

Let the equal quotient 1.97° be added to both values 138° and 130° : There 
are then presented the two values (130° + 1.97°=) 131.97° and (138° + 1.97°=) 
139.97°. As preliminary to the application of these values the following re- 
marks are offered : Let the earth's surface be measured, and 42° arc, most 
unquestionably, will be found to be a governing, or often, very often, repeated 
measure or boundary of the earth's surface-divisions. Generally, over the 
globe 42° arc, east and west, (in difference of longitude), or as running at the 
normal angle of thirty degrees, is the measure, from shore to shore, over 
ocean, and from coast to coast over land. Let instances be now given, although 
they are repetitions: The dotted line of 42° arc reaches across Australia over 
land; it spans the breadth of the Mediterranean sea over water; it reaches, in 
more than three positions, from Nova Zembla to the continent over an ocean. 
From the shores of the Great Lakes of North America, and from the shores of 
the Caspian and Aral, of Asia, this measure reaches alike to Northern oceans. 
From the bottom of a deep bay of the east coast^f Asia the line reaches over 
land and water to the shores of the Siberian islands. Look on the eastern coast 
of the United States: three of these dotted lines bind together the windings of 
a southern and northern coast. And where these dotted lines do not measure 
the extents of the terrestrial masses, there the volcano's blaze is a beacon to 
mark an incomplete uprising of the land from beneath the ocean.* 

Has this measure of 42° arc an astronomical origin? There has been pre- 
sented two values derived from astronomical elements, to wit, 139.97° and 
131.97°: 139.97° divided by 3.332,— which is the ratio of the number of the 

*The statement was omitted when this subject was before under discussion, that the position 
of volcanoes, as a general law, is on the newer geological formations — on those formations, the 
more recently elevated, which fact supports the position of the text. One other remark should 
also be madG: Continents are raised and depressed (as is universally admitted) ; then it follows from 
the continuity of God's works, that minor parts are also relatively raised and depressed, for there 
is no per saltum change of action in Nature ; the parts move as entire continents. 



earth's days in a year to the number of the sun-diameters of distance, earth from 
sun, and the quotient is forty-two degrees; 131.97° divided by the ratio of the 
circumference of a circle to its diameter, 3.14159, gives also a quotient of forty- 

There is now presented the fundamental origin or foundation of the ratio of 
one to sixteen, which first was traced out as the ratio of the oscillation of the 
obliquity of the ecliptic to its mean; then, used to calculate, from the sun's cir- 
cumference, the value of the earth's diameter, and also the value of the ellipticity 
of the earth's figure; and afterwards employed to produce, from as many times 
as the moon's distance from the earth contains its diameter, (109.62), the 
governing value of the earth's surface structure, to wit, 138° arc ; from which 
the measures of the terrestrial masses, 84° and 42°, were derived. Let the 
following be specially noted: as 1 is to 16, so is to be found the ratio of the 
sun-diameters in the mean distance of the earth from the sun, (109.6,) to the 
number of the days in the earth's year, (365.24). Thus this ratio is founded on 
the ratio of the days of the year to the distance of the earth from the sun, to wit, 
3.332, which is 3.14159 flus T ' T . This arises from the facts, that the earth's axial 
equatorial velocity is to the sun as 1 to 4.34 + ; for, 14.5, the number of the sun's 
rotations in one year, -*- 4.34+ = 3.1416 plus T ' T or 3.332, and that 365.25, 
times the earth's diameter, is equal to the sun's circumference, plus T \. 

Say that, by measurement, 138° is found to be the major axis of the conti- 
nents. The moon's distance is then measured and is found to be 109 6 times 
its diameter. 109.6 times the excess of the earth's equatorial circumference is 
130° arc. These are the data required, then: 130°: 138°:: 3.14159: 3.332; 
365.24-3.332= 109.6; 109.6 x 870,167 (the value of the sun's diameter) 
= 95,375,000 miles, which is the mean distance of the earth from the sun, cal- 
culated from the earth's structure and distance of the moon. 

To find the circumference of the sun (giving the diameter as used in the 
preceding): 110,340, is the number of the years of the revolution of the sun's 
perigee or ellipticity of the earth's orbit, 110,340 x 26.227 miles, (the value of 
the ellipticity of the earth's figure) = 2,904,600; 3.332 : 3.14159 : : 2,904,600 : : 
2,733,650, which is the value of the sun's circumference. 

Therefore, by the use of the distance of the moon as co-efiicient, both the 
distance of the earth from the sun in sun diameters, and the value of the diame- 
ter of the sun have been calculated from the earth's divisions and surface struc- 
ture; and the former, the distance of the earth from the sun, can be calculated 
from the structure of the earth alone. 

From, therefore, the earth's structural divisions aud from a knowledge of 


the value of the fundamental element of the solar system the amplitude of the 
earth's orbit can be calculated. And before this, was not the distance of the 
sun from the earth in its mean truly calculated from the surface divisions of 
the earth only? 

Why should it be doubted, that this can be accomplished? A priori, and 
on general principles, it is sound philosophy to believe, that while the distance 
of the earth from the sun was determined by law, so also was the structure of 
the earth's surface thus determined; and why not then by the same law? And, if 
by the same law, most truly there must be relations between the measures of 
the heavenly spaces and the terrestrial spaces. Therefore, all philosophical 
considerations lead to the conclusion, that it is possible to discover these rela- 
tions, so that a measure on the face of the earth may respond to a measure on 
the face of the heavens. 

Even if the idea were visionary only, it is a vision of the exceeding great 
power of God, which power, directed by wisdom supreme, from the action of a 
few simple laws, constructs the huge mammoth and also a living organization 
so minute as to be many thousand times its bulk below the lowest range of the 
human eye; which constructed an Astral Centre, so immensely distant that it 
is seen and known only in the light of philosophic induction, around which 
Astral Centre, the sun, with its attendant planets and their satellites — the whole 
solar system itself — most rapidly revolves; from the centre of this mighty 
revolution, came to the sun, the value of the inclination of its axis; from this 
element of the sun came to the earth its inclination of axis; from this degree 
of inclination, or in other words, from the obliquity of the ecliptic, is derived 
the structure of the earth's surface: so that a mere island-rock, in mid-ocean, 
serving only as the nestling place for ocean birds, step after step upwards, link 
after link of the chain of harmonies which binds together the whole universe as 
one — this little island, has, in its position and bearing relatively to other masses 
of land, a relation to and with the Astral Centre of the revolution of this solar 
Edifice of Worlds. What forbids this union in our minds of the great and 
minute, of the transient forms and the eternal fabric of the heavens? Is it too 
bold? What is there which is too bold or too aspiring when the human mind 
considers the laws of the Almighty God, who provides not only for man, as 
an individual, but has arranged the surface of the earth for the well being of 
the race ; who, not only numbers the hairs of our heads, but has in His memory, 
every minute appendage of the globe. 

The question, even at this late day, is sometimes asked, what is the use 
of scientific investigation and of the philosophic speculations of the action of 


God upon His worlds ? The reply is ready. The study of science elevates the 
mind, and gives to it a world-wide expansion, so that the beautiful harmony 
and wonderful sublimity of the almost endless extent of things subject to man's 
view, throw back into his mind beautiful, high, and holy thoughts. 

Kepler was the first man who, for centuries, dared to go back "as if noth- 
ing had been done in the way of theory." He loved harmony and order; and 
he sought in the outer world that which would answer to, and deepen, the order 
and harmony of his own thoughts. For seventeen long years, undiscouraged by 
accident and delay, he urged forward his inquiry, through failure after failure; 
and at length was rewarded by seeing for himself, and opening to the sight of 
others, the harmonic law of the planets of the solar system. Because he died 
in poverty and neglect, was he unhappy, and was his life a failure? The answer 
is in words uttered by him on his bed of death: "I thank thee, my God! for 
the exceeding great joy which the contemplation of Thy works has given to 

When seeing the glory, and the harmony of the motions of great spheres 
which fly through space with such intense rapidity that thought itself can 
scarce keep up or move on with them ; pondering on the great wisdom requir- 
ed in the formation of their orbits, and on the Power Supreme by which they 
are held to these orbits; thinking of space as if there were a wasteful profusion, 
it being only dotted over with stars; struggling to grasp the thought of infinite 
time as shadowed out in the swaying back and forth of worlds, which, as the 
pendula of eternity, in their oscillation, mark the years, centuries, and ages of 
time; witnessing the whole creation subject to fixed law, — all its parts moving 
in unbroken sympathy as with one common pulse of motion: then, there is felt 
the great joy for which Kepler poured out his thanks ; 

"For the man, 
Who in this spirit communes with the Forms 
Of Nature, who, with understanding heart, 
Doth know and love such objects as excite 
No morbid passions — no disquietude, 
No vengeance or hatred, needs must feel 
The Joy of the pure Spirit of Love."